BA makes it so that it is not necessary for the DM to make checks, saves, AC, to hit scores, etc. more and more difficult as PCs gain levels. It has, by and large, de-emphasized the "treadmill effect." This is a point that DMs need to be aware of, especially if they cut their teeth on prior editions of D&D. DMs need to remember that they don't need to boost the numbers because it should get easier for players as they gain levels. What makes it more difficult is that they will be faced with more powerful/deadly effects. For example, a beholder's disintegration ray, a more damaging trap, a creature that can attack 2 or 3 times a turn rather than 1 time per turn, creatures that can cast spells.
As for skill use, as DM, when I analyzed the DCs of most of the playtest and early adventures for 5e, I found that nearly 80% of the DCs were DC 10-12, while about 15% were about 15, and only 5% were 20. This was a revelation for me, basically because I used to set DCs higher for the most part. I found that with most of the lower DCs, BA worked really well. It encouraged nearly any PC to attempt to do things that in 3e (without the skill trained), the PC would never attempt. As a player or a DM, I never really felt that I was not capable of accomplishing things. If the majority of the skill checks stay below 15, I think that most players will not ever feel as if they are not improving as they gain in levels, and of course, as others have stated, it really is the rogue and bard who shine when it comes to dealing with skill checks.