I agree.
A bonus is a bonus regardless of the source. If you want to add more meaning into each bonus and DC, then you have to start changing the entire system. So a save DC must always check the attribute or class to obtain more meaning and the attack roll must always account for the level of the attacker with martial classes having a greater impact.
What makes more sense is increase the bounds to add more distinction, except you must account for all the sub-systems that rely on the bounds, which is probably just as difficult to manage.
You don't have to change the system. You just have to be creative with how you use the system. I've been having fun with the 5E skill system using it to highlight characters and add cinematic flair to otherwise boring skill challenges. My players don't mind it at all because the number one rule is make it fun. Everyone rolling a die for everything isn't fun. It's tedious and ruins verisimilitude, especially on ridiculous rolls like the wizard with the 8 strength rolling a natural 20 to knock a door down while the half-orc with the 20 strength fails. Not cinematic or interesting at all. That is what you get when you run things where the DC rolls have an objective meaning.
I'd rather have it so that being a big, strong guy has an objective meaning as in there are things he can do that no one else can even attempt. Why should a scrawny gnome wizard with an 8 strength even get to roll to burst an iron bound door? He wouldn't be able to do it at all compared to the huge 6'6" and 300 lb. half-orc. What about a skill or a physical feature like size having an objective meaning? A flat roll alone does not mean something has an objective meaning. In fact, it makes it seem like skills mean nothing or physical size means nothing because anyone with a lucky roll and a couple of attribute points can do the same thing as a person that has physical attributes or areas of knowledge the other person does not even possess.