Identifying cold-starts is a huge win here, using something to keep your lambdas warm is important for user-facing functionality. That functionality alone makes a compelling feature.
There seems to be a lot of book-keeping and ritual for something which is supposed to just let you focus on the important bits of code, without worrying about how it runs.
Having said that, I agree that there seems to be an inordinate amount of effort/thought going into keeping Lambdas "warm" (i.e. always running).
I think the prevalence of these hijinks indicates that AWS Lambda should consider adding a "keep running" option that ensure the particular function is always "warm", but costs a bit more.
Might as well containerize it and accept the overhead of some maintenance to ensure the lowest cost guaranteed availability and performance.