Except for running out of VM space, all the other issues are still there. And even if you have (for the time being) practically unlimited VM space, you may still not want to mmap a file of unbounded size, since setting up all those mappings takes quite a lot of time if you're using the default 4 kB page size. So you probably want to do some kind of windowing anyway. But then if the access pattern is random and the file is large, you have to continually shift the window (munmap + mmap) and performance goes down the drain. So I don't think going to 64-bit systems tilts the balance in favor of mmap.
Linux allocates page tables lazily, and fills them lazily. The only upfront work is to mark the virtual address range as valid and associated with the file. I'd expect mapping giant files to be fast enough to not need windowing.
Good point, scratch that part of my answer.
There are still some cases where you'd not want unlimited VM mapping, but those are getting a bit esoteric and at least the most obvious ones are in the process of getting fixed.