A +1 represents very little progression in abilities (an increase of 5%), so, in order to feel like an expert, bonuses have to grow to a larger value (+10 or +15) to achieve that feel. The advantage/disadvantage is a good attempt to moderate this problem, I think, and another of 5e's successes. But 5e still does not really solve the underlying problem, which I think comes from the changed use of the d20 in D&D...
+1 on 1d20 = +5% is true, at least from a certain perspective. But while it's a popular way of looking at it, it's not a particularly useful one. Note this is more a general comment than anything else, using your post as a springboard. It's not really about your post, or even the d20 system.
Say you succeed on a 19+ on a d20. That means in two cases (19, 20) you succeed, and in 18 cases (1...18) you fail. How does a +1 affect that? A +1 has a minimal effect on your chances of
failure, reducing it from 18/20 to 17/20. That works out out to a 5.56% reduction, which is pretty close to the +1 = 5%. But not the same, and that's because it's a very different way of looking at things. To show how different, consider the other end of the spectrum. With a +1, you now succeed on a 18, 19, or 20, not just on a 19 or 20. That +1 means your chance of
success has increased by a whopping 50%.
The reverse happens when the chance of failure is low. If you succeed on a 3+, that means you fail on 1 or 2, and a -1 means your chance of failure increases by 50% (since you now fail on a 1, 2, or 3).
In most RPGs, there's usually a low chance of a very bad effects happening (classic D&D saves are an exception, at low levels), and a high chance of a most routine things happening. For example, your chance to hit tends to be clustered toward the top end of the scale, where a +1 matters a lot more than it does in the middle or the bottom of the scale. Conversely, if there's a low chance of something really bad happening, then a -1 matters a lot more because it greatly increases your odds of failure. In other words, a +1 tends to worth a lot more than 5% when it comes to things you're fairly competent in, and a penalty matters a lot more when there's a small chance of something bad happening.