Proxy baptism the way Mormons practice it does not solve the issue at all. The overwhelming majority of people who have ever lived are now lost to history. Are they not worthy of salvation?
Christians believe in baptism by desire for those who were never formally baptized, not proxy baptism. For example, in A.D. 256, Cyprian of Carthage wrote about baptism by desire. You can also read about it in certain catacomb encryptions. So it is clear from the beginning they believed in baptism by desire.
There were a few sects that believed in literally baptizing a dead body. But from the evidence we have today, proxy baptism was never mainstream or widely practiced. The idea salvation can only occur if you were lucky enough to have your genealogy recorded is far removed from mainstream Christianity.