You can have your I/O and Doom graphics on the Turing tape no problem. What’s different is that accessing an arbitrary position on the tape isn’t O(1), like no

You can have your I/O and Doom graphics on the Turing tape no problem. What’s different is that accessing an arbitrary position on the tape isn’t O(1), like normally assumed for memory, On the other hand, memory (and address space) on real-world computers is finite, so you can always find a large-enough constant to make the Turing equivalent O(1) again.