Is taking the SAT four times too many (and if so, why is it the case) in the eyes of college admission people?
I cannot speak for college admission people. I have never been one, and I probably never will be. That said, you should not worry about how many times you take the SAT.
Historically, folk wisdom was that one should not take the SAT more than 3 times. This may or may not have been true back when there was no such thing as score choice and you could not stop schools from seeing how many times you took the test. The concern was that students who took the test too many times would look test-obsessed, and therefore not well-rounded.
Nowadays, that’s a non-issue. Schools only see the scores you send them. So while there are still arguments for not taking the test a million times, how it looks in the eyes of admissions people is not one of them. (There are some schools who ask you to send all your scores. If you’re applying to any of those schools, then you should be a bit more judicious in deciding how often to take the test.)
One final thought here: People usually only ask this question when they’ve already taken the SAT a bunch of times, and often their first time was “cold” and “just to see how they’d do.” Please don’t do that. There is no reason to pay for and lock in an official score you’re not going to want to use. Take practice tests to see how you’ll do. Don’t take a real test until you’re ready. Then you won’t have to worry later about an unknowable thing like how your number of tests looks to a total stranger.