OP, this is a good homebrew rule to talk to your DM and fellow players about. Some tables prefer to keep it as-is, citing that it picking between the two makes for a meaningful choice. Others, me included, prefer to have their cake and eat it too. It'll make your campaign feel a little bit more high fantasy, with a party of adventurers that all have 20 in their main stats. For many, that's a positive.
If your DM is comfortable adjusting encounters for a party with maxed stats and a couple extra feats, it's (imo) a great rule to run with.
In my experience, having stuck with CR religiously, you find yourself with tense, anyone-could-die sessions - against a pack of wolves from a random encounter. And then you have easy, bring it home encounters - against the arc's big bad. It takes control of the fight's narrative stakes out of the DM's hands, and makes it more-or-less random.
I want to stress that it was fun to play this way, but eventually myself and my players longed for more dramatic final encounters, and so I had to homebrew creatures.