I don't think it's technically possible at all. There are very different platforms with different consensus mechanisms, different fees structures, levels of centralization and other things like that. Not to mention that lots of altcoins are completely worthless, so if such an integration were possible, they'd greatly benefit from it, and others would suffer from it. Overall, it's just a very bizarre, confusing and very anti-decentralization idea which, luckily, will never become reality. If such a thing happened, I think there would be too many coins of a currently (the merged one), the trust would fall significantly, and the market would shrink.
As to me the main thing is that is really anti-decentralized and that's why will never be done by crypto community. But as for technical possibility it is possible in theory by series of iterations of hardforks with integration of data from one ledger to another one. I don't see any reason in such merging and radically against it but can see a variant how technically it can be done.