The other thing you're forgetting when you want to say let's do
10X - 0.9 = 9.9 - 0.9
instead, is that as valid a step it is, it's not the only valid step you can do there. Which can make some other proofs, especially those involving trig functions and powers of such, rather nasty, since if you do the wrong step (which is still valid) at a certain place, you can make the equation more complicated or end up going round in circles instead (and proving something equals itself), instead of actually doing the valid step you need to get to the result you're trying to show
