An aperiodic PRNG is impossible on any real computer. It’s perfectly possible on a computer with infinite storage; alternately, a real computer can run a PRNG with a long enough period that it’s for all practical purposes aperiodic.
Note that there are a lot of PRNG that do not repeat. That has nothing to do with being a real or pseudo RNG. (You just don’t want to think in terms of memory limits.)
One difference is between having a secure crypto system and not having a secure cryptosystem. That seems very practical to me.
“Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.” John von Neumann
Love this comment: "Such a terrific reference work! But with so many terrific random digits, it’s a shame they didn’t sort them, to make it easier to find the one you’re looking for. "