ad_hoc
(they/them)
It would probably make for better gameplay, but I would caution that the shoving/grappling system is one of the rules I have to explain to people most often (nearly every time it comes up), and that's without them then having to know this "grapple save DC" which unlike a comparable spell save DC is not used for a lot of things. The main problem is that most people (at least most not playing barbarians) shove or grapple once in a blue moon and rarely used rules are the hardest to remember.
Then again nearly every table I've played at had or has someone who can never quite keep straight exactly how bonus actions work and those happen every damned turn.
If they are shoving/grappling all the dm needs to do is ask for str mod and proficiency bonus.
If the player is being shoved/grappled all they need to do is make a strength or dexterity saving throw.
It is actually easier for the player and I think neutral complexity for the dm.