I don't think it's been mentioned ITT, but the spell Shield is often integral to keeping concentration. It provides a huge safety net against getting hit
-it can be cast as a reaction, after you know you've been hit, so you don't waste spell slots on it
-it adds +5 AC until the start of your turn, a big bonus that possibly negates multiple attacks against you that would otherwise call for Con Saves
If shield was added as an actual reaction, not as a pre-cast option like feather fall, then this would massively help keeping Conc.
At upper levels, I think serious changes would have to be implemented along with any concentration changes. High level spells are just too powerful too allow multiple of them at the same time.
--e.g., The ability to cast Greater Invisibility & Fly would basically make a caster invincible. No one would realistically be able to target them
