Margin of success and crits in D&D 5e

Forget about combat for a second; this will be about critical success and failure when rolling ability checks and saving throws (if you want to read what I think about crits in combat, try this post). Specially, it complements my last post in a way.

Paga 242 of the DMG has some interesting rules about the subject (emphasis mine):

DEGREES OF FAILURE
Sometimes a failed ability check has different consequences depending on the degree of failure. For example, a character who fails to disarm a trapped chest might accidentally spring the trap if the check fails by 5 or more, whereas a lesser failure means that the trap wasn't triggered during the botched disarm attempt. [...]

CRITICAL SUCCESS OR FAILURE
Rolling a 20 or a 1 on an ability check or a saving throw doesn't normally have any special effect. However, you can choose to take such an exceptional roll into account when adjudicating the outcome. [...] For example, rolling a 1 on a failed attempt to pick a lock might break the thieves' tools being used [...].

As you can see, this rules are very free-form and a bit odd. Both rules deal with the same subject, but it isn't clear how they interact with each other. Maybe a natural 1 is worse than failing by 5 or more, which is strange since someone can be unable to fail by 5 or more (if your skill is high enough and the DC low enough) and still roll a natural 1. Or maybe they are just different things. Trying to open a trapped chest? Well, you can break your thieves' tools, spring the trap, both, or none.

Also, there seems to be no "degrees of success" rule, just "degrees of failure", which seems a tad unfair (well, unless you see this section as a way of giving a "second chance" after a failure, which might be the point). Of course we can apply a similar reasoning to both situations... but that causes another strange effect.

See, now MOST rolls (55% to be exact) are either greater successes or greater failures. "Ordinary" results become the exception. If you need to roll 14 or more to succeed, anything lower than 10 is a greater failure and anything over 18 is a great success.

The way I see it, most result should be ordinary, with a few criticals now and then. Now only because it makes sense, but also because coming up with "special" successes and failures get old fast... and they're not so special if they come up every time.

Fumbles should be rare

My easy fix: an exceptional success or failure only comes up if you beat or miss the DC by 10 or more. Yes, this means that if you're good enough you cannot fumble, and if you're bad enough you cannot crit - but if you want this possibility, you can still use natural 1s and 20s in this way (or even "confirm criticals" if you want; I hate this mechanic for combat, but it works fine for skills).

Simpler, faster, easier to calculate, makes more sense.

It also fixes my problem with the medusa of the last post - a miss by 10 or more means you fail AND must save again immediately. So there is still a chance of immediate petrification, but it will be rare and mostly reserved for weaker character.

Same thing for skill contests - succeed by 10 or more and you get an immediate roll "for free" against your opponent, and vice-versa (if you're rolling against yourself, get a "free shot" to get another success that doesn't count as a failure if you roll badly). Works for grappling too.

There is plenty of other ways to play around with this. For example, it might make rolls that are too easy or automatic successes have some meaning - of course you'll succeed, now you're rolling to see how awesome you look while doing it.