I'd be asking - is this harmful to my equipment?
If you have an AG pool, it's probably ok, however, an IG pool with a heater etc in line, the concentrated bleach running through the plumbing can do much damage to anything metal - rot your heater etc.

I'm guilty of adding through the skimmer regularly, it works for me because removing a 30 foot round cover is a bit of work, and the pool is an AG so there isn't much that will corrode.
As for the solar cover, only the section immediately above the return died and is now a half circle that I cut out (about 1foot by 6inches), and this happened year 2 when I was also aerating and shooting the water up, nothing has changed since then on the cover - no worse, no better, and we're on year 4 now.