What are the implications of disabling PMing until some minimal requirement is met to reduce spam?

I just received a spam PM from an obvious spam account with no questions or answers. I copied the content and informed a Mod of their username, but it made me think that this kind of spam is preventable for the most part. What if you had to earn the privilege of PMing someone other than a mod (I could see how conversations with mods could be necessary for someone new to the site) by meeting some very minimal requirement such as 24 hours after posing at least one question or answer that didn’t get deleted. In other words, you can’t spam others until you’ve at least participated minimally on the site and have waited 24 hours (or possibly only a couple of hours) so that fake posts attempting to satisfy those requirements would have had sufficient time to have been screened out.

Would implementing this have some negative consequences that I’m not seeing? Obviously it would require coding/testing resources, and that’s not an insignificant thing. I’m just thinking it might have the potential to save the mod team a lot of time/effort down the road.