I cannot envision a problem that a checksum in the HTTP protocol would fix that TLS wouldn't also fix.
You have to ask yourself "How would this get corrupted"? If the concern is that the data ends up somehow mangled from an external source like a bad router or a lose cable, then the data simply won't decrypt correctly and you'll end up with garbage.
So that leaves you with an application bug. However, an app is just as likely to add a checksum for an invalid body as they are to add one for a valid body.
So, the only fault I could see this fixing is an application which, through corrupt memory or something else, manages to produce a garbage body which fails it's checksum but... somehow... is encrypted correctly. I've never seen that sort of problem.
You have to ask yourself "How would this get corrupted"? If the concern is that the data ends up somehow mangled from an external source like a bad router or a lose cable, then the data simply won't decrypt correctly and you'll end up with garbage.
So that leaves you with an application bug. However, an app is just as likely to add a checksum for an invalid body as they are to add one for a valid body.
So, the only fault I could see this fixing is an application which, through corrupt memory or something else, manages to produce a garbage body which fails it's checksum but... somehow... is encrypted correctly. I've never seen that sort of problem.