"Fixed" for what purpose? Full mobile wallets?
This would be unlikely, but I'm open to persuasion.
I don't know what you mean by "full" mobile wallets. Full node? If so, then only Moore's law will give us that, and it probably will. I don't know how far back you have to go for today's mobile devices (quad core CPUs, 64 GB of storage etc) exceed a typical desktop PC, but it isn't that far. You won't have to go far into the future for a mobile device exceed today's typical desktop computer, and the latter is certainly capable of running a full node.
If you mean some sort of method of operating a lightweight wallet on a phone that is short of a full node but doesn't rely on a trusted server, that is being worked on. I'm explicitly not promising this will succeed and there is no promised delivery whatsoever, so don't start calling this vaporware. I'm interested in a persuasive argument if there is one, that it "can't" be done.
Furthermore there is work being done to directly reduce the size of the blockchain itself, which is what I meant. I guess it could be argued that gets closer to there being a full node on a mobile device (i.e. trims some time off waiting for Moore's law).