You can use Mailinator to do this already, you can see all of their inboxes on their website and you can use all of their domains to bypass domain restrictions.
For example I might use somethingsilly@bobmail.info and it will be redirected to https://www.mailinator.com/v3/index.jsp?zone=public&query=so...
While I'm a fan of Mailinator and their approach, I think the feature OP has about auto-clicking verify is unique. But yes, to do this right, you need the multi-domain approach of Mailinator instead of just aliases. Maybe Mailinator has an API or supports POP/IMAP that would make this possible, I haven't checked.
You can easily use one of many opensource self-hosted temporary email projects with APIs. Just check Github.
Receiving email is pretty easy - own domain with MX record and some cheap VPS with Docker. No need to worry SPF, DKIM, DMARC, DSBL - you care about these when you have to send emails from the host.
Last I checked it appeared like Mailinator's POP3 support was completely removed, and API access requires a subscription. It was priced way above what I was willing to pay (I think $150/mo)
Also Mailinator is banned by multiple sites and I feel like that number is increasing (anecdata). Which means it's getting less and less useful for the purpose of "burner" email addresses.
I used Mailinator as the quick solution to access some one time resources on websites that forced me to register. It was the simplicity of the throwaway email that made it attractive to me. But when it's blocked on a website I usually wouldn't want to bother with c more complicated setup. If the effort is justified then I can probably use a regular email address. Other people might have different use cases.
I don't know if it still does it, but mailinator used to have a neat feature where it would "detect" bots trying to scrape its list of domains and start injecting legit ones like hotmail.com/gmail.com
This is probably much more difficult and taxing. On every signup, you're now checking MX records and IP's, not just looking at a string. And Mailinator can change this information regularly too if they choose.
well for one you also need to blacklist the aliases, ex. guerillaclick+sdf@gmail.com, and i suspect sysadmins start showing more hesitation when you need to start pattern matching (risk of false positives and additional overhead)
While I'm a fan of Mailinator and their approach, I think the feature OP has about auto-clicking verify is unique. But yes, to do this right, you need the multi-domain approach of Mailinator instead of just aliases. Maybe Mailinator has an API or supports POP/IMAP that would make this possible, I haven't checked.