I've read this question, but there isn't an official (reasoning) answer there.
I do realize that when I post fast, or when I change IPs I keep getting asked to prove my humanity, but I want to know why. Doesn't logging in prove it enough?
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No, logging in is not enough. A program can log in (there are plenty of web scrapers that do just that) - but a program will find it much harder than a human to solve captchas as well.
It really is for everyone's benefit. It helps you because its unlikely the same person would sign in from one country one day and another country the next. It helps the whole community by preventing bots from spamming everything. Just be thankful they have a readable captcha because I've seen much worse.