I wouldn't say 50% is necessary...there's definitely some leeway.
But suggesting that water changes can prevent a cycle is pure nonsense.
I agree with this and say 25% weekly is good, I would not do 50% with this currently stock though. 30% maybe at the most.
As long as the water is clean the fish will be fine. If your stock increases or there are water quality concerns/disease I do agree to 50% changes.
I had a customer once who was trying to fight their cycle and doing massive daily water changes it delayed the cycle from completing since the levels of ammonia continued to build on a daily basis. This isn't the case here. From reading over this it sounds like this is mostly due to the stock either coming in poor or already sick before you bought them, nothing on you.
This is the game that we all play to keep our fish alive and well. All of us have our different tricks and tips that work for us. I hope that the tips that others have posted here will help with the issue at hand and that you will enjoy the hobby as all of us do.