I think as you do. I would find a cover flattering, as long as that cover doesn't produce income without a license. A free fun thing on youtube would be fine by me.
However, if an artist covers my song and makes $20M, being that it's my song, I would expect some of those dollars. Not all, for that artist performed my song, and they own the performance and the "spin" or "flavor" they put on my song. But it is my song.
Speaking of which, I wonder, does it cost a lot to get permission to cover a song from a major publisher for broadcast rights? Has anyone tried to get permission to cover a song and broadcast it?
You can license music from various places, including ascap and others. This was the problem in the 80's where rappers were "sampling" tracks and putting their own lyrics over existing music - without permission.
And yes, the original songwriter should be compensated for those sampled tracks, and yes, often times that sampling brings new life to the original, un-rapped track.
The exception is advertising commercials. Best I can tell, you can "steal" commercial music for an advertisement without issue, without even giving a credit.
GM did that with their "Chevro-lation time c'mon" ads for about five years in the early to mid 90's - not one dime to the orignal songwriters.