From a personal opinion standpoint, I agree with your latter statement. I don't block throwaway email domains from my services.
The few times I've hosted something like this (previously running open source https://gitlab.com/markbeeson/maildrop), it just never ends well.
What typically happens is abuse reports start rolling in for mass forum spam, mass registration, comment spam, domains get blacklisted and added to global blacklists like URIBL.
Over time as bad actors found it, I eventually was doing more than 50-80 Mbps of _purely text traffic_ of bots flooding registrations, inbound SMTP traffic of nothing but spam, bots effectively sending DoS-level requests looking for activation links. It was frustrating to want to run something fun and inevitably end up spending half your day responding to "this is a development/testing INBOUND ONLY mail service, we did not originate the spam, we are not signing up 5000 times to your forum", adding a domain blacklist to never show messages from certain websites, etc.