It's not really gaming the system if the assumption is that most saves will have proficiency.
What it does instead is encourage a cinematic style of play.
If you say so.
I think it encourages players trying to come up with imaginative ways to get a +2 to +6 bonus where the rules do not allow it. +2 to +6 is huge.
I'd rather players take the Resilience feat or the Lucky feat or try to acquire Inspiration or quest for items to help with their saves as opposed to modifying the rules.
At higher level, doing this is like handing out a bunch of free Inspirations (possibly per day depending on who they fight), regardless of how the players roleplay.
On top of that, it can become a pita for the DM when every player thinks that s/he can just dive behind furniture in order to get a save bonus on Fireballs or other Dex based attacks, etc. Once Pandora's Box is opened, it changes player's expectations.
Before throwing in this powerful of a house rule, you should probably play the game into the mid to higher levels first to see if you are solving a problem, or creating one.