Hard to salvage parts when every time they lose a battle to the Covenant, the Covenant hang around to glass a planet and then that system is more or becomes enemy territory. Arcadia is a rare example of the Covenant NOT fully glassing a planet, and the Gettysburg at Reach was a fluke.
Resources would be better spent focusing on trying to build new ships and materials, not wasting lives and time trying to go in and salvage stuff that is probably so destroyed it can never be repurposed again. I mean you're looking at high-gee close combat where metal is constantly under pressure, against an enemy whose primary ship to ship weaponry MELTS hull armor, or slices through multiple decks at a time. It is all under high strain and what isn't being melted or blasted apart will most likely lost it's structural integrity from tumbling around in space, through debris fields, and since the UNSC likes to fight with their backs against planets, subject to the gravitational forces pulling against their momentum and the eventual de-orbiting into the atmosphere and burning up from a uncontrolled descent.
It's not worth it to the UNSC to try recovering lost ships.
Now Insurrectionist elements, however, might just be stupid or desperate enough to make a run at some of the lesser damaged ships, whatever few would left after a battle. They could maybe salvage a little bit of stuff assuming they got there immediately after the Covenant finished glassing a planet and before the ships began to fall to earth.
But yeah, not really something they do.