I don't think .at is mismanaged, quite the opposite, but in the way of many ccTLDs it is a little bit eccentric. I don't know why route53 might not support them: perhaps it's to do with contractual faff, or possibly because nic.at uses a less common flavour of EPP.

(Sadly the common flavour of EPP has a bonkers data model; a few ccTLDs use an alternative model with a more sensible data model, but although the more sensible flavour of EPP is easier to use in isolation, it has the downside of being different from the ICANN flavour.)

Why would you not be able to add an .at domain on route53? It’s not like there’s any difference from the dns point of view.

Is it .at blocking the nameserver changes or AWS refusing to serve .at domains from their nameservers?