It works well for peace of mind as it gave me a high degree of confidence that I'm testing almost exactly what the end-user would experience. However, it does add 5-10 seconds of delay to your tests while polling the email inbox, it can be a little expensive depending on your test frequency, I think there are even some cases where you can hurt your email deliverability stats during automated email sending.
In the end, I decided to keep this test manual which I run every now and then only after making big changes. Instead integration tests which mock the email service are probably enough for my use case.
Curious how do others test the end-to-end behaviour of their web application, when it comes to emailing?