It's also important to realize that the standard Turing machine doesn't actually have an infinite tape, but rather it has a tape that can grow to hold an arbitr

It's also important to realize that the standard Turing machine doesn't actually have an infinite tape, but rather it has a tape that can grow to hold an arbitrarily long, but still finite, sequence. At any point during the execution of the Turing machine, only a finite part of the tape will be occupied. So we can construct approximations of it in the sense that we can create computers with varying, finite amounts of RAM. This might seem like a pedantic/obvious point to make, but it is actually also possible to design abstract computational machines that operate on truly infinite quantities, like a machine that has random access to an infinite, uncomputable sequence. From a simplicity perspective, it also makes more sense to consider machines with an arbitrarily large amount of RAM (you can always hotplug more RAM), compared to setting some arbitrary limit because that is the most RAM we happen to be able to achieve in this universe.