I wouldn't recommend it. Saying "anytime" actually means something, just like saying "no problem" means it wasn't a problem. If you want to satisfy a grammar curmudgeon you need to use the meaningless formality that only "You're welcome" can convey.
Why do you care about this? There's never been a social standard for the saying after thank you. I'm not sure if one could be even implemented or is necessary. You must be bored.
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