While I'll second that this works absolutely perfectly fine, I will say there are some small benefits to adding more diversification. Beyond the math impact, it conveys something to the PCs when you set a DC. Often, that distinction won't mean much, but sometimes it tells a story. My little notes on setting DCs focus on setting a DC baed upon how much luck someone trained in the effort would take.
An easy task (DC 10) is something most people do not screw up, regardless of training, unless they're under pressure (DC10) . A DC 12 (moderately easy) task is something that amateurs generally fail at, but you can do with a little training or natural skill. A moderate task (DC 15) is something that you often do not get right unless you have training - I think of it as entry level professional tasks.
With that in mind, why would setting a DC of 12 versus 10 or 15 have an impact on a game? If players understand how I set DCs, which is publicly available information in my rules, it can tell PCs about a scenario. For example, the PCs come upon the corpse of a humanoid lying at the base of a door. They talk and come up with the hypothesis that the door might have been trapped. They search and find it and I tell them it was moderately easy (DC 12) to find it. What have they learned?
1.) The trap on the door was not well hidden. It was not good enough to hide from a journeyman professional, but was fine to stop the rabble.
2.) Despite being not terribly hard to find, the corpse at the base of the door did not find it. That means they were likely not trained and didn't have any natural skill in finding traps.
Could a DC 15 have worked? Yes. But not as well. It would have conveyed that an entry level professional was necessary - and that it highly unlikely that an amatuer, even with natural skill, would succeed in finding it. That is different. It paints a different story about who and why the trap was set, and who the corpse might have been.
It is not a huge impact, but we find it meaningful in my game.