If it is the kind of site for which you are willing to keep a cookie around, then you'll only have to get a new link from your email whenever your cookie expires or if you explicitly log out.

Otherwise, you are correct.

Anecdotally, everyone always has their email open anyway (I do, everyone I work with does, my family aways does), so the extra step of checking your email is trivial.

Unless you use a different account for junk websites than you do your day to day email. I have my work email open all day, but not my personal email, which is also different to my spam email account I use for trials or junk websites. If I need to have 3-4 different email accounts open just to manage my sessions, I could see this being a massive pain. Also if I sign up using my work email to a work related service (so I can use it at work), I might not have access to it at home.

If you use gmail, you can be logged in to multiple accounts at once.

The thing is I'd log into my email anyway to check for new messages.