The case for Fifth Edition Saving Throws in old school

I was thinking about saving throws this morning, as I've been slowly working on a house rules document.  I've always dug the original saving throws, and how they scale depending on your race or class.  When I first played Fifth edition, the first thing I thought was "where are the old saving throws?" (as in second edition or earlier).  They just didn't make sense to me at the time.  As well the 3rd (or 3.4? not sure) saving throws of Fortitude, Reflex and Willpower made some sense to me but not a lot.  As an example where do these modifiers come from? My guess is Fortitude is constitution, Reflex is dexterity and willpower is wisdom? Which make sense, as I can't think of a reason to have a charisma saving throws (or atleast I don't think it would come up very often to me).  While writing the document, I thought okay I'll just go ahead and use the 3 saving throws, the modifiers for this will come from the stats listed above.

However, that means there's no intelligence, charisma, or strength saving throws. That and having either a mod or just a static number doesn't appeal to me either.  As an example, a willpower saving throw would just be the wisdom stat or the wisdom modifier.

I also detest DCs.  Having done roll under ability checks, I prefer that idea.   The problem becomes when reading a OSR set of rules like Labyrinth Lord, or B/X the saves are roll over, and the ability checks are roll under.  It is sometimes hard for players to grasp that.  (atleast my players).

What I came up with, which I'm sure is not an new idea, is to throw out the original saving throws (vs spell, death, etc) and just use ability scores as checks.  The mechanic is the same, roll under.  Let's say a player is near falling off a cliff and trying to grab onto something, well you can call it whatever you want, an ability check or a saving throw, whatever the case roll under dex.

So rather than create 3 saves from 3e, or the originals, or just one saving throw (which I've been a fan of, but I like this idea better).  Just go with the 6 stats.  Need to make a death saving throw? Make that tied to Constitution.  Which makes some sense anyways. The guys that created DND were on the right track with the 6 ability scores.

Moving forward I think that's how I'm going to approach it.  For one thing, when you are using DCs its very easy to hand wave, unless a player rolls a 1, as they don't always know the DC number.  Whereas roll under, it's entirely up to them, and its rolled right on the table.  I think this gives a bit of player agency.