In my humble opinion. You should lower your expectations for blockchains from US exchange sites. I have reasons why there won't be native tokens on BASE or INK.
Firstly, I don't think there will be a strict competition between Base and Ink blockchains. This is because those blockchains exist for the service expansion purpose. They're not being made for profit-oriented purpose.
Secondly, it is most likely Base and Ink Blockchains won't have their native tokens. US-based exchange sites have operated them. They won't be illegally issuing the new security that doesn't meet US's law.
It's important to remember that Coinbase has launched its IPO. Its stocks are now listed on Nasdaq.
Also, Kraken seems to try to follow the same path by preferring to launch IPO instead of issuing the new crypto. And in my understanding, they are strictly prohibited from issuing another security. So, there will not be native tokens for their blockchain products.
Of course not. If Gary Gensler still heads the SEC, we shouldn't expect Kraken nor Coinbase to issue their own tokens. They will quickly face pressure from the regulatory agency by listing "unregistered securities". Only a Trump win will move the crypto industry forward. If things get "tough" in the long run, the aforementioned exchanges can move to another country with crypto-friendly regulations and launch their own tokens from there. So long as it's outside the US jurisdiction.
Considering that both INK and BASE are based on the same scaling technique (Optimistic rollups), I wouldn't expect them to compete that much in the future. They're very much alike. Except that one of them will be more popular than the other. The Ink Network is just getting started, anyways. Who knows how long will it last?