I haven't used SES in over 2 years now so things may have changed but lots of ISP's blocked the emails. Even basic transaction type emails.

Also, if you send over 10k too soon, you may be throttled or shut down. Lastly, they also throttle you if your bounce rate is higher than 2%. To get around that, you must make sure your list is super clean or send emails slowly to make sure your bounce rate is not over 2% in any given month. Not ideal for newsletters or large customer lists imo.

Again, some of this may have changed since I used them 2+ years ago.

Not OP but I've heard (anecdotally here and there) that many sites reject email from Amazon IP blocks because of historical spam problems.

I only encountered it personally a handful of times when using SES for delivery, and it was usually resolvable because the target customer base was easy to reach and worked with their IT departments to solve the problem.