Based on my 30 or so hours of playtime, I would approve of changing stats to be background deterministic. It would make a clear divide between the non-combat oriented backgrounds and the combat oriented ones. Right now they just have some base higher stats and events, with a huge price tag upgrade in comparison to say a wildman or brawler (which are currently on their way to becoming my favorite backgrounds).
Would this discourage the use of some backgrounds? Absolutely, but it also won’t encourage people to play the high priced backgrounds as much either. Think about it:
If you want a tanky character, you can easily go with the farm hand or the hedge knight.
If you want a melee dps character, you can easily go with the killer on the run, hedge knight, sellsword, adventurous noble, wildman or brawler.
If you want an archer dps character, you can easily go with sellsword, a witchhunter and I’m sure a few others.
Which means that each background still has its own inherent value. Are there a few that have very little use? Well yeah, but they can also be cheaper to be used as cannon fodder. Your first few hires are probably like that anyway, fishermen and such, whatever you can find and afford.