I'm just trying to wrap my mind around a very different mindset of D&D.
So, for example, if it's someone's background, letting them add their proficiency bonus to related tasks/knowledge from their background (that aren't already covered by other skills/proficiencies)?
Maybe letting players learn a profession (equivalent ability to being able to doing the checks with their background) with the same time/training rules for learning a language or a proficiency in a set of tools?
Like with my soldiering example, if it wasn't their background, but if during the campaign if someone spends 250 days in a regular army, let them gain essentially "proficiency" with soldiering and be able to use their proficiency bonus on appropriate checks?
The change can certainly be daunting, especially if you liked the more measured bits of past editions. I thought I did at the time, and then I played 5e and felt like this huge weight was lifted off me.
My world was now my world, and I didn't have to worry about some preexisting rule that I may or may not agreed with. If I envisioned something to be different, BAM. Done.
Now, I personally love, LOVE, world-building. And when I saw a lack of professions as you suggest as a possible issue that meant I got to decide how things work to some extent.
For example, some of my players expressed a desire for professions. Something far more granular that the current rules would adequately support.
I designed my own herbalist/potion crafting system for one, and for a couple others a whole fishing enterprise, and how that would work, what the challenges could/would be.
Did it mean I had to get off my duff and learn way too much about either topic in an appropriate time frame? Sure. Developing and running those two new systems was sorta fun for me. And more so when the players enjoyed the work put into it. I can understand if someone doesn't find that same enjoyment, or has that kind of time (I honestly don't think I spent much time on it, aside from some Wikipedia/research rabbit holes I fell into).
I feel like 5e opened up the world for me to tinker in it. And not having rigid rules for a myriad of professions and skills was certainly a big part of that.
I mean, thank the gods I don't have to worry about both a hide and move silently check anymore.