Although my husband has received some tips, he more often sees the same scenario you described, Diesel. You'd think the pax would have enough SA to realize who was doing the work. Yeah, Go Figure.
Seems to me that the company should stay out of it entirely. It's a private expression of appreciation from the pax to the flight crew. Of course, if the companies wanted to point out that their pilots were so badly paid that tips would be used to supplement the pilot's low wages, that'd be helpful.

Instead, when the subject is addressed by the company (at least at NJA) the practice is discouraged. After all, they're anxious to perpetuate the myth that their pilots are all professionally compensated. They can do something about low wages. They just choose not to.