In making my tier list, I tried to make it as objective as possible. To do so, I tried to measure their utility in the hotel's operations (RD and valley) and the major story routes they provide.
Leader seems to be the indisputed best background for me. The major contributing factor would be the ability to get THE extra companion to stay (Pedro and Nikos). An extra companion is immensely useful in racking up points in RD and exploration. Moreover, this also provides much more plot/content. Getting the two biggest personalities to hunker down? OP!
Arts is ranked A-high for me because of a similar reason in Leader-- this lets you get an extra companion. Extra companion = extra points daily + more content. (Plus it has the best T-shirt)
Tech is also ranked high, but I'd rate it lower than Arts. This is because of the free tech point it gives you everyday. Over your playthrough and the length of the game, these tech points will stack up!
Humanities has a similar effect with Tech, but I think it's worse. This is because of the presence of Asterion, who is woefully stuck at RD while you're not hanging out with him. Our moo is good with contracts as he's been exposed to them in centuries, while his tech could use some work. Ask yourself, would you rather be helping him do contracts or covering for his tech? Try playing Math and see those accumulated contract points compared to tech and you will easily come up with the answer.
Math and the one below is significantly worse, I'd wager. Math makes you good at planning ahead-- which is kind of an almost useless skill in this game. Why? The metagame spits on the abilities of a numbers man. Want to know how many days you need to complete this route? Check the wiki. At least you know how many points you've saved up? This isn't actually that good of an info; it doesn't really matter until you need them and meet the requirements. Finally, the save-load system is what really wrecks it. Math can see which combinations it will need to get that upgrade at that day, but so can a time-traveling reloader. Incidentally, save-reloading also allows you to manipulate the chance to get double the materials found in the valley everyday, which is a blow to Math's privilege of gathering materials (during accounting?) with Themba.
Speedrunner is kind of the same place as Math for providing no benefit in obtaining points for upgrades. I haven't actually seen the event for speedrunner turning a danger event to its benefit, can anyone explain? If it's abusable, it may be better than Math in some respect.
In making this list, one can see that extra points reigns supreme in the rankings. This is because it makes you achieve goals quicker (by having more points). An extra companion is at the top because it's 3 to 4 extra points every day compared to no-benefit backgrounds. The passive 1 point per day of Tech and Humanitarian starts out earlier, but will be overtaken by the extra companion as the game drags on. This may change if the hotel will have more than 7 workers (because of the current 3 person/activity limit + hanging out), which will give a slight edge to the passive unconditional 1, as opposed to a wasted companion that stands idle not contributing points. At the bottom would be the backgrounds that have no access to these extra points at all. Each day that passes makes the gap that separates them even wider, leaving them in the dust.
But hey, this is just an attempt at an objective tier list for an optimized playthrough, which is to say nothing about the fun all of the backgrounds have! No doubt the devs would balance out enjoyment between all the routes beyond game mechanics, so rest easy. Anyone with their own list and thoughtd?