What other options are there?
[PDF Warning] https://apps.dtic.mil/sti/pdfs/AD1161973.pdf
Maybe a future version of the catcher would have a large/refillable gas tank that lets it catch things, change their trajectory just enough to hasten their descent, and then continue on mission?
A no-fuel way to drag things down would be even better, like the sibling comment talks about tethers. Imagine a catcher that attaches a tether line that slows down LEO objects purely by drag.
Adjusting orbits to match multiple satellites is a tough requirement, with a heavy delta-V cost. Especially more so if it needs to get to a deorbiting trajectory in between each catch.
I'm frankly not even sure how to napkin math such a question.
LEO velocity is about 8km/s.
Plugging that in to mv^2 gets you about 200 trillion joules of kinetic energy.
Assuming the chemical (burning) energy contained in space debris is negligible, that 200 trillion joules is the maximum energy you’d transfer to the atmosphere if all this debris suddenly deorbited.
The sun, in contrast, transfers about 430 quintillion joules per hour to the earth[1].
So the kinetic energy of all LEO mass is about a millionth of the energy the Earth receives from the sun every hour.
Prob not a heating concern.
(Please check my math. This was a wonderful nerd snipe but I did it on my phone while defrosting chicken nuggets).
0: https://www.sciencedirect.com/science/article/pii/S009457652....
1: https://thatsbyers.com/blog/how-much-energy-does-the-sun-rea....
Also the vast majority of the energy in an orbiting body is not in gravitational potential energy (not that you said that) but in the kinetic energy of the object moving at something like 4.75 miles per second.
The end result is that the energy an object decelerating back into atmo releases is about the same magnitude as the energy of the rocket that got it up there in the first place.
But the energy we put in was with an efficiency below 25 percent (I would guess) so the energy it will release will be equal to a fraction of the energy we put in plus the energy released from oxidizing whatever burns on the way down. But still probably less than it already had put into it.
TLDR inconsequential effects. Not enough mass to matter. 5200 tons of space rock falls on earth every year.