The issue of memory bounds is commonly handwaved away. Note that your desktop computer is technically not Turing complete either, since it only has access to a

The issue of memory bounds is commonly handwaved away. Note that your desktop computer is technically not Turing complete either, since it only has access to a finite amount of memory+disk storage, and is thus a (very large) finite state machine since there are only a finite number of states it can be in.