I suspected this might be your method. There are a couple of regular posters on this forum that play this way. It's looks to me like a fiat-based mishmash of Success At a Cost, Degrees of Failure, and Critical Success and Failure (DMG p. 242) combined with the Roll With It approach (DMG p. 236) and methods from various other games. Many DMs accumulate their approach over the years to deal with specific issues that have arisen in the way they play without ever taking a hard look at the underlying problems or considering whether the approaches that they accumulated are necessary in their current game.I agree. And I think one of the biggest differences is, as mentioned, I use die rolls (dare I say "skill checks") as a narrative tool all the time, so this idea that you should only rarely roll and only when the stakes are high is antithetical to my DMing stye. So, even if the 5E DMG says "don't roll unless you have to" I ignore it because those dice inform me of things.
For example, if the PCs are looking for a silversmith (an example that came up early in the thread) I will have them make a check (I usually give the players a choice between a couple things, such as Investigation or Persuasion, or simply let them tell me which skill they want to use and explain how they are employing it). Now, a low roll on the check does not mean they fail to find the silversmith and got lost looking for it. Chances are, I had not given the silversmith a single thought prior to this moment. So, instead, the low roll on the check tells me something about the silversmith.
Maybe they found it but it is closed. Why, it's the middle of the day? Trouble, I'll wager. What kind? The kind that will drag the PCs in, for sure.
All that sort of thing flies through my brain in a couple moments and becomes part of the game world from that moment on. For me, after years and years of doing it this way highly successfully, this is a far superior outcome than simply saying "Yes" or "No" because this die roll -- coupled with whatever other context was happening in play -- told me something about the world. I would have learned something else about the world had it come up very high or right in the middle, too. There was no "DC" at all, and the task was trivial, but the result of the roll wasn't.
Personally, I find this a kludgy way to play as compared to what we've been discussing and particularly hard as a player to judge what the outcome of a roll is going to end up being which means it's harder for me to apply any player skill to the game. The way I would have to deal with this is to pump my skill and tool proficiencies as high as they will go and then push to make those rolls only which is pretty much how I remember D&D 3.Xe being played by any player with a passing familiarity with the rules. I don't see how one can get to this approach by a plain reading of the rules of D&D 5e and I find a game works better when it's being played in a manner that the rules suggest.
But, of course, if that's what you and yours are used to and enjoy, then carry on. Something like this may have been for 2005 me, but 2020 me is playing a different game.