Linux already overcommits memory so much you can imaging it's infinite, the big show-stopper is the 64 bit integers used to track it. We'd need infinite pointer sizes before we could meaningfully use infinite tape.
Turing machines don't have pointers, just offsets from the current position. Since you can't move infinite steps, you can still use finite offsets.
Good thing is there is no halting problem when using 64bit pointers.