1) you MUST NEVER remove the pipes with any process. If you are, you need to research more and find out how not to...
Every time I service the rear end on my Valkyries - prior to placing the bike on a lift - I remove both sets of pipes and the various footpeg hardware.
Why?
They get inspected, cleaned and detailed.
You are most welcome to do what ever you wish on your own bike.
If you wish to, as you do, use it as a means of cleaning them, then that is a great method, rather than laying on the ground and working up, and this is giving you an excuse to do the job right.
On mine, if you loosen the rear hangers, you get enough flex to clear the axle.
Remove the exhaust, so you replace the gaskets every time? Then the chance of over tightening those exhaust studs and breaking them, another cost. (I've removed the studs and used antiseize and my drill, and ran them in-out to clean/free them out).
Then there is the described method of removing the shocks and lowering the swingarm. Outside of the special items for the job, no additional costs.
But the questions was to remove the exhaust to remove the rear tire, so that would mean remove the rear axle. So it still stands. It's not required.