OK, you are correct about 4 people per stateroom not being a problem, and I agree that if steerage passengers can carry enough food and water on board to last the trip, that is also no problem, provided there is some sanitary facilities or the ship's own recycling system has enough room to store the, uh, used water.
Hmm, looking over some materials, it seems that the concept of steerage passage was introduced in MT for Hard Times, prior to TNE. Arrival Vengeance has a scenario where a subsidized merchant is carrying economic refugees "packed into the hold, shoulder to shoulder." How many people can be packed into the cargo hold of subsidized merchant? Maybe 100?
The problem, as I see it, is not bringing along what they will use in the trip i.e. food, water--heck, even O2 could be brought in compressed canisters. The problem is getting rid of what they've used, and I don't just mean the sewage. With every breath each one takes, they are passing CO2 and water vapor into the air. IIRC correctly from my days as a hospital corpsman, the water loss from respiration is greater than that from perspiration and urination combined. All that exhaled water goes into the air. Likewise the exhaled CO2.
As it builds up, the exchange of gasses in the lungs becomes less effective. We are able to get the metabolic waste CO2 out of our bodies through simple diffusion in the lungs--the CO2 flows from an area of concentration (blood carried to the lungs) to an area of lesser concentration (air). When the CO2 level in the air gets too high, this transfer will no longer occur. At least, that's how I remember it from many years ago. Wasn't this one of the crises faced by Apollo 13?
I don't say that it would be unfeasible to install equipment to deal with this, but I do feel that simply "packing them in like cattle" would be a death sentence, not a rescue, and of course, any starship captain would know this and refuse to take more than his/her ship could handle. Something like a full life boat refusing to pull anyone else out of the water.