Is there any reason why we can't have self-gassing tokens?

One of the biggest headaches/obstacles in ethereum's widespread adoption insofar as I can see is that it's a nuisance to have to hold some base token in addition to whatever ERC-20 people wish to hold.

Seems to me like a fairly solvable problem with smarter smart contracts. For example:

• I wish to send some USDC but I don't have any ETH. It's impossible for me to swap the USDC, because I can't send it to a DEX without gas
• A DEX offers a smart contract wherein by signing; I "promise" to send USDC once it's broadcasted. If I sign it, the contract fronts me a little bit of ETH, and then promptly takes some USDC from my wallet in return. I've already signed for this and there's nothing I can do to prevent it.
• In fact, as I understand it, the DEX can simply broadcast and pay for the contract itself which includes the transaction I wish to post, plus a little extra going back to them. All without ever having to send me anything

The whole encounter is totally trustless. Polygon has a 'swap for gas' feature which is pretty handy, but seems to be very centralized in nature, and an additional layer of complication which is a lot to ask of many prospective users.

Really I don't see why a feature like this can't be baked directly into the tokens themselves. Imagine a world where tokens can automatically and transparently convert some of themselves into gas.

My inspiration for this post is that although this is something I've been wondering about for a while as I learn more about this technology, I recently read this article by coinbase which kind of vaguely hints that they're working on tackling this very issue.

Anyway, I can understand why circle is slow to actually pull the trigger on rolling out complex updates to their multi-billion dollar coin, although it does state in the article that there is a mechanism in place to amend their existing contracts, but I still find it interesting that no DEX that I know of has incorporated a feature like this. In my view: it looks like someone stands to make a lot of money by developing this system.