Serverless is essentially PaaS, basically shared-hosting
Serverless as AWS Lambda, simplified operations, but essentially PaaS, so basically the old shared-hoster with know from Perl and PHP haydays. (btw PHP7 is great again nowadays)
About AWS Lambda, I was quite underwhelmed by it's crude implementation. One has to re-upload a zip file with the complete source code, again and again. Even shared hosters that have support Perl and PHP since 1997 have been more advanced and offered FTP or upload form where one could re-upload only the altered source code files, not the whole repo everytime.