I feel as though the momentum you are describing is essentially driven by buzz around Bitcoin, and as such may be mercurial.
The momentum is driven by bitcoin's economic advantage of being the lowest transaction-cost currency for online and distanced transactions. People choose bitcoin over altcoins then because they want the most compatible cryptocoin, the one that has has mass-approval, this is the network effect that says that a network is more valuable to new people the more people that are a part of it--and bitcoin is by far the more important crypto network. And once they've chosen to invest in a coin with both money and merchant services, they're less likely to give other altcoins the same chance, this is path-dependence.
Beyond that, the network effect and path dependence both work in confluence to create a synthesis effect that drives new people towards bitcoin and away from altcoins the further development there is in bitcoin, the more adopters, etc.
Sidechains are the cherry on top, essentially cementing all altcoins subservient to bitcoin and reliant on it for future survival. Darkcoin will become a sidechain for privacy. Namecoin becomes a sidechain for real-estate. The penny has dropped and bitcoin has won the altcoin war, much as we predicted years ago.
Btw, the analysis of path dependence and the network effect giving bitcoin the unbeatable adoption advantage comes from brilliant economist
Peter Surda's 2012
master's thesis on bitcoin, which I recommend to you.
The assumption that bitcoin's popularity is driven by buzz and not by economics is what drove the various scoffer crowd and the like to create memecoins, specifically Doge. They believed they could out-buzz bitcoin and thus either surpass it or perhaps some thought to destroy it.
However the devs that controlled Doge's code were ignorant that economics was driving bitcoin, not doge. They had no idea why people really liked bitcoin; they thought it was being new-cycle pumped and they decided to outpump bitcoin.
What began as a joke became serious as the coin gained some value. Ultimately they signed the death-knell of doge by removing the limit on coins created. Bitcoin is partly what it is because inflation is not in the interest of users of currency, but the Doge people didn't understand this, and thus Doge is now dying or dead.
Would there be anything to stop me from taking Bitcoin code line for line and adopting it as a large institution with an interest in developing a means of online transaction?
Absolutely nothing, but there are many reasons why this is unlikely to go anywhere. To put it bluntly, bitcoin has already drunk your milkshake. Path dependence of those who already bought into bitcoin sucks up the oxygen. It would be like trying to create a new fax-machine network on an incompatible protocol and convince people to buy your new fax-2.0 machine. Unless it has something the other fax machines can't do, then it has absolutely no chance of gaining mass adoption.
Such thinking has led entire countries to try to create their own cryptocurrency, ala Ecuador, and they're going to learn a difficult lesson thereby in the long run. It won't work for them nor solve their currency problems.
I could list off many further reasons why sponsored altcoins aren't a threat to bitcoin. Probably the biggest is that path dependence of people already into bitcoin prevents their widespread adoption. The network effect means a network is more valuable the more people that buy into it. That's something you can't just copy in terms of code. That is to say bitcoin isn't just code but an ecosystem-complexity, and you can't duplicate those other elements that drive bitcoin adoption.
In fact, sidechains in bitcoin integrating altcoins adds all altcoin's network value to bitcoin, making it more valuable than any one of them could ever be individually.
From here on, all altcoins will have to have a unique purpose that isn't the focus of bitcoin. None of them that survive should be focused on being a currency on their own and little else.
Perhaps countries like Ecuador will survive with a locally-approved cryptocurrency that functions by clearing internationally as a bitcoin sidechain. If that's what the future holds, if all countries go that way... things could get very interesting. But if they try to issue more cryptocurrency the way they issued fiat, they'll find repudiation happening yet again.
This isn't even to address the question of development and security and market confidence, which also can't be duplicated by simply copying code.
I know what's going to happen if there's a sudden fault in bitcoin's code, I've seen it happen and seen it resolved, bitcoin devs jump to the computer and solve it before I even know there's a problem, and I know there are extremely smart coders out there working full-time on improving bitcoin's system and adding features. These cannot be control-pasted into a GIT repository either.
What do I know about your fly-by-night altcoin? That the devs controlling it could make a Doge-quality decision and kill it overnight?
I know that no one can remove the coin-limit on bitcoin and create inflation because mining protections prevents it. But if your entity is doing all the mining initially, as it must to start out, you've essentially already 51%'d yourself, with no guarantee that you'll ever convince enough people to buy into mining your system to ever change that, plus no one accepts your altcoin. Bitcoin spent years facing this wall, and companies like Bitpay have been operating for years now. You can't duplicate those either.
Only by buying into the sidechain system can you make your coin relevant to the larger bitcoin ecosystem, and even then you only cement bitcoin in place as top coin, not the reverse.
It seems to me that an entity able to generate sufficient buzz could easily side step the entire market in this way and render other cryptocurrencies obsolete (other than as a means of online black or grey market purchasing).
It can't be done as a mere cryptocoin, because a competitor cryptocoin has no competitive advantage over bitcoin and cannot theoretically gain one, because both bitcoin and every cryptocoin are just code, and what one code can do another code can do.
Any feature an alt-coin could develop could be implemented by bitcoin if it ever became important enough to threaten bitcoin's market position. And there would be plenty of incentive to do so.
The result is bitcoin would squash the altcoin like a bug, adopt their feature and it's over for them.
Aha! But what if they don't open source their currency and thus bitcoin can't copy their technique?
That's an even bigger problem. People don't trust secret code, and trust is the name of the game. Look at the problems that Darkcoin has had getting going, and most people, including me, like their proposal! But without a code review who can say if it's got a real solution or not.
It's the same reason the dollar hasn't been superseded as a currency for decades now, it has very little to do with the actual paper dollars are printed on--all fiat currency can do the same things other fiat currencies can do, why isn't the Canadian dollar the world's reserve currency instead?--rather it's the US system, economy, confidence, and military power, etc., that makes the dollar what it is on international markets. The system-complex > the thing itself alone.
Which is why the only possible challenger to the dollar is a currency of another mode that can do what the dollar can't possibly do.
And digital crypto is that mode, cryptocurrency is that entity. Cryptocurrencies can do things that fiat currencies cannot do, like transmit themselves with their value over communication lines. This is the key to their lowering of transaction costs, and thus their compelling value-proposition.
I promise you, it's a brave new world we're entering, and questions like yours are important to ask, however they should diminish in doubt with each passing year that bitcoin grows in strength, important, value, adoption, and influence.
Bitcoin will become the dominant world currency eventually, for these and many more reasons, and we are living in the midst of a revolution perhaps as important to humanity eventually as the invention of the computer was to last century. Things will never be the same.