There's also the thousand cuts - if you want a big server, you will have to do lots of discussion and arguing about the cost there of, but if instead you're adding a small monthly cost, the arguing isn't as much.
You keep doing that and suddenly someone notices that half the budget is AWS, at which point the "move onsite" dance begins (until the next time the big server argument happens).
Write big checks for big servers every few years Vs Recurring monthly out the door slowly growing, but maybe 2x higher in total
Also flexibility in not having to do capacity (or much of any other) planning.