I think the marketing is aimed mainly at technology management, not developers. Obviously, they have to evangelize developers, too, to a certain extent because they need a critical mass with familiarity so that the managers aren't saying “that’s nice, but who do we hire to build stuff on it”, but developers aren't the ultimate target of the marketing for serverless or most other cloud technologies.
I'm also starting to see the term LaaS (Logic as a Service) used as an alternative to "Serverless" here and there.
LaaS sounds much more accurate/palatable.
I haven't done much reading up on it but it basically sounds like someone else is hosting and executing your code?
The message is "you don't need sysadmins anymore", which is exactly what developers want to hear.
It's also very good for the cloud vendors, because with noone in the sysadmin role, developers are far more likely address scaling issues by just throwing resources (money) at the problem.