Similarly to how Tesla's future failure or success is irrelevant as they've already succeeded in the most important task of proving that EVs can work and thus driving the industry to produce them en masse, Uber and Lyft have driven a revolution.
They've shown that the old model for running a taxi service was horrendously outdated and customer-unfriendly (and also driver-unfriendly, in some cities) and now others can innovate and compete along the same lines, differentiating via areas that Uber and Lyft either can't or won't. I know it's essentially a meme on here to diminish Dropbox or Twitter to being basic services that one could easily replicate in an hour or a weekend, but it's similar for Uber and Lyft: the underlying concept and technology is relatively easily replicable - meaning their moat is pretty insecure. As time goes on, one can envisage them dying a slow death by a thousand cuts.
From a consumer's perspective, some sort of federation or interoperability would be needed between these competing apps. If it is necessary to research and download a different taxi app for every city --including going through the usual painful signup process each time-- it will drive people back to the common denominator of the big incumbents.