Maybe it's not that they won't do it but that they don't have to.
Of the HOT sisters, Arieth, Elena, and Heather don't do it, but maybe their tuition is already paid for because I don't think it's a pre-requisite that all HOTs have to not have it paid for. Riona, Sarah, and Melanie maybe do need help with paying which is why they're part of Quinn's business.
Of the HOT daughters, Camila has joined up and Mona likely will too. Lily seems like someone who would as well, Ashley's uncertain about it because she needs tuition money, and neither Maya or Josy know about it yet.
So joining Quinn's business could be conditional on tuition status; those whose tuition is paid for don't have to do it if they don't want to, but those who want their tuition paid for by the HOTs must join up or be kicked out.
I find the finances of the HOTs extremely confusing. At first I thought Quinn was embezzling money from the sorority to buy drugs, then using the proceeds from her restaurant to pay it back. Simple enough, and the 'rumor' about free tuition was just part of her plan to grow the take-out business. But I don't think that theory holds up after Episode 4.
We learn that Sage is worried about the HOTs solvency in part because Quinn has accepted an unprecedented 6 daughters. Later on, Sage agrees to Quinn's still unrevealed plan to raise money for the HOTs (though she is clearly unhappy about it). What exactly does Sage think this money is for?
We know Sage doesn't approve of using drugs in the HOTS house, and she seems not to be a drug user at all. I think it's reasonable to conclude she is not (knowingly) using sorority funds to buy drugs. So there must be some 'legitimate' expense that she is worried about.
She mentions they collect dues from the sisters, so it seems like more sisters would mean more revenue. The HOTs obvious expenses (the house and all the cool amenities within) are relatively fixed; we've certainly seen no plans to add additional bedrooms or anything like that.
The only things I can think of that would scale with membership would be the costs of food and 'HOT' branded clothing. We see Arieth cooking at one point, so I don't think they pay chefs and my expectation would be the girls buy their own groceries and frequently share the food. The clothes are definitely an expense, but I'd be shocked they were a large one.
So then I was wondering if maybe the HOTs *do* actually pay for sisters' tuition, and they just kept that a closely guarded secret until Quinn decided to start luring in new blood. That explains Sage's concern, but how the hell would a sorority pay for that? I guess they could have a massive (yet secret) endowment, but in that case you'd think Sage would be a hell of a lot less laid back about membership applications. She may prefer to leave things up to Quinn, but she certainly isn't stupid. When an applicant is s 6 digit expense, you don't just fast track everyone who shows up.
Then I wondered if Quinn's restaurant wasn't her own side business, it's actually standard HOT tradition to finance their way through college and Sage just doesn't run it anymore. That could make for a Shocking Twist(tm) down the line, but it still runs into the old problem of why more girls is an issue. If the sisters turn tricks to pay for their education, more girls should be revenue neutral. Sage should be worried about obvious weak links like Maya and Ashley rather than the total number of daughters. (This also runs counter to the way Sage is unhappy if the MC knows Lily only through her work at the Pink Rose.)
I'm really hoping Episode 5 will shed more light on this situation because at the moment it makes no sense to me.
