It has been clarified through comments that this would be applied per-site, so someone posting on Seasoned Advice wouldn't interfere with someone else posting on Programmers. With this clarification, I support the proposal, at least on a trial basis.
But if traffic on Programmers increases anywhere near Stack Overflow levels, this would begin to interfere with on-topic use of the site. The 90-minute policy at Stack Overflow combined with the exhaustion of IPv4 addresses has already caused problems for users behind network address translation (NAT). When you have the same IPv4 address as another user of the same Stack Exchange site, it can be tough to squeeze in your question when others are waiting for the same 90-minute window to reopen so that they can squeeze in their own questions. See, for example, the question "Error — 'you can only post once every 90 minutes' but I haven't posted in daysError — 'you can only post once every 90 minutes' but I haven't posted in days" by Bryan on Meta Stack Overflow.
Why might people be behind NAT? Some people access the Internet at a school, office, or public library, which typically has one Internet access subscription with one IP address. Others use an ISP that puts multiple subscribers behind one IPv4 address using carrier-grade NAT. CGNAT is common in countries with smaller IPv4 allocations and on cellular Internet.
Comments to the answer to Bryan's question recommend subscribing to cellular Internet access and asking the question through that connection. This ignores cellular CGNAT as well as the added cost of a subscription to cellular Internet access. I thought not having to pay for ExpertS-exChange was why the Stack Exchange network was created in the first place.
Thus without the ability to ask or answer questions before 125 reputation, a new user would have to farm rep by suggesting edits and have 62 accepted just to be able to use the service as intended.