There's no reason you should have to remove them to clean the cage to an acceptable standard with them in. The tray will be the main thing, which you do daily. Any toys or perches can be removed one at a time, slowly and carefully, cleaned and returned- one by one.
Then wipe over any bars.
I do the same as Therm and Faery Bee for a few days at a time but once a week move Peta to a small travel cage to have a more thorough wash & disinfect of everything. That would be tricky with Peta left in the cage, as she is so nosey & gets seriously in the way
The way I transfer her is to make sure she sees me putting some millet berries and spinach leaves into the travel cage. Then I put both doors together & open both. The lure of the treat in the travel cage makes it no problem-- she hops in.
With the reverse, it's the same procedure, visibly & obviously putting treats where she will want to go to find them. There is usually no bird- handling involved at the transfer, unless it coincides with out of cage free time.
My intention is always to check on her weight while she's in the smaller cage but I often forget . I would normally weigh the cage with her in it, then again when empty, then do the maths...that's the most difficult bit!