I dunno, I think it's probably fine to have
Untrained (+0) - Apprentice (+2) - Journeyman (+5) - Master (+8)
to match the untrained, jack of trades or racial bonus, trained, trained and focused rules for other skills. You could have the 4th tier as you say, and make it +10 I suppose (racial or path +2 plus trained plus focus, to match the rest of the system)
The trick is determining how 'many' and to what extent you can have the background skills. To that, I think it varies wildly by game. I'd cheerfully allow folks to just pick a few and just write them down and never call for rolls, but that's not other's cup of tea.
So, the DM should pick a number of background points for people to have, from 0 to 10, and people should put 1-3 in each skill. So in a campaign where people are teenagers just going off on their naming quest, they can have 1. In a campaign about ex-war veterans turned upstanding citizens coming out of retirement to save the kingdom it can be 6, etc.