Oh, I see what you mean. That sounds quite easy to work around, actually. Due to the speed of light, only a section containing the disruptions to the repeated pattern need be considered for the initial state; and then you can compute outward from that.
https://en.wikipedia.org/wiki/Turing_machine#:~:text=Cells%2...
Whereas the Rule 110 Cyclic Tags engine requires the infinite tape to contain infinite repetitions of structured patterns, even in order to simply run "while(true)". That's a key difference.
I also agree with zamadatix's sibling comment.