It shouldn't be done, Uniswap solves a problem that cryptocurrency made for itself. Otherwise, Forex trading has been a thing for decades. Failing that, I might be pedantic enough to suggest that it is possible. "The Blockchain" is just a single permutation of many data structures that could handle such a workload. Hell, you could even use PGP signing to replace a Blockchain altogether, designing a peering system that works similar to proof-of-stake, but without the append-only database or mechanical transaction signing. There are hundreds of such theoretical systems that would have no problem handling this, and I think it's pretty silly to assume it "can't be done". Bittorrent navigated a similar problem space without using a Blockchain. IPFS tackled a bigger problem space than cryptocurrency, and implemented things better than a Blockchain would have. By rejecting a Blockchain, IPFS was able to add sophisticated features like versioning, pinning, high-performance DNS resolution and peering that actually scales.

I think you're overestimating how hard this is to fix, and the utility that the Blockchain is providing in something like Uniswap.