Serverless is a marketing term for CGI, and you can observe that serverless is very popular.
A couple of years ago my (now) wife and I wrote a single-event Evite clone for our wedding invitations, using Django and SQLite. We used FastCGI to hook it up to the nginx on the server. When we pushed changes, we had to not just run the migrations (if any) but also remember to restart the FastCGI server, or we would waste time debugging why the problem we'd just fixed wasn't fixed. I forget what was supposed to start the FastCGI process, but it's not running now. I wish we'd used CGI, because it's not working right now, so I can't go back and check the wedding invitations until I can relogin to the server. I know that password is around here somewhere...
A VPS would barely have simplified any of these problems, and would have added other things to worry about keeping patched. Our wedding invitation RSVP did need its own database, but it didn't need its own IPv4 address or its own installation of Alpine Linux.
It probably handled less than 1000 total requests over the months that we were using it, so, no, it was not significantly better to not fork+exec for each page load.
You say "outdated", I say "boring". Boring is good. There's no need to make things more complicated and fragile than they need to be, certainly not in order to save 500 milliseconds of CPU time over months.