It does however affect getting updates from government agencies, and others who insist on only disseminating real-time information to the public via Twitter.
For instance: https://twitter.com/WakaKotahiWgtn
This is the account for traffic events (road closures, traffic accidents, etc) in my city. Not signed in, the latest visible post is from February 2023.
Since I don't have a twitter account, this is now functionally useless.
Without giving Amazon too much of the benefit of the doubt here, I've noticed they love to offer you "coupons", generally with a midnight expiry.
I expect it's 100% a tactic to get you to commit to something you've looked at a couple of times but might be on the fence about buying.
I get the same as OP's logged-out price (nothing hidden) while logged in, perhaps if they are offering a coupon it would take it below the minimum advertised price.
Definitely stupid, but it's the only way I can see of arriving at this situation.