I agree with you that they aren't really "important" to most people. Which is unfortunate, because I always like to see our athletes succeeding whether it is in basketball or golf or tennis. But are students going to be ok paying student fees if they know it's going to the golf team? Probably not.
As for why lower division sports are less expensive, there are a host of reasons why FBS programs spend much more money.
First, as you mentioned, there are less scholarships at the lower levels. Even FCS football is only allowed 63 scholarships as compared to the 85 of FBS. But as you go lower, there are even less. Here is an interesting website I check out every now and then to see the difference in scholarship limits per sport/per division.
http://www.scholarshipstats.com/ncaalimits.html
Also note that only Division 1 football, basketball, volleyball, women's gymnastics and women's tennis are head count sports. Meaning that all scholarships are full scholarships, not partials. Every other sport can split their scholarships up as many ways as they choose.
Other notable reasons why lower division sports are cheaper:
Travel - most D1 teams fly a lot, most D2 and D3 teams never or hardly ever fly,
Apparel - D1 athletes get hundreds, if not thousands, of dollars worth of gear; some lower division athletes have to pay for their own,
Food - catered buffet meals vs. Subway,
Lodging - D1 athletes usually get their own bed, D2 and D3 many times put 2 athletes to a bed.
Finally, enrollment sports are a thing in D2 and D3, not in D1. In these sports, the team has a minimal budget and their goal is to bring in tons of athletes to go to the school, play their sport, but most importantly pay tuition. Administration doesn't care if these teams are even successful, as long as they minimize spending, keep their grades up and noses clean, and bring in lots of students.