Agreed. This is a perfectly rational argument against participating in a frequent flier scheme of any kind.

If you're paying for your travel out of pocket, then buy the flights that make the most sense for you and forget about frequent flier programs altogether. In the long run, you'll come out ahead.

If work pays for your flights, or you can bill them to someone else, then concentrate your flying on a single carrier (or at least, a single alliance) to maximize your potential benefits.

There's really no magic to any of it.