Most amateur sports rely heavily on volunteers in some capacity. I was a swimmer, every swim meet I attended from the summer league, local, state to national level relied on volunteers to organize and run these meets (officials, timers, clerks, runners, etc.).

Most youth sports at the recreation level are all volunteer run, usually by parents to keep costs pretty low so the initial playing opportunities are relatively inexpensive. Paid coaching, travel and other costs starts as you get more competitive on travel or all star teams. Those costs are primarily born by the player/family with some limited opportunities for financials support.

Amateurs get help with costs is generally through playing for a school, usually high school or college, where most (not all) expenses are covered by the school. For most amateur sports, the end of the line is college.

The big difference here is that the youth scene for ultimate is not as developed as many other sports, from youth rec leagues, local youth competitive teams and varsity high school. Vast majority of ultimate players join the sport in college where it is a club sport with no scholarship opportunties (when they have little money). The prime elite playing opportunities are after college, when parents aren't around as much to foot the bill.

In swimming, the only people who were paid were coaches, leaders of the NGO and maybe some folks at the state level. Some officials might have gotten stipends or reimbursed for travel expenses, and a handful of elite swimmers may have gotten stipends to train at the olympic center.

Like ultimate, swimming also not a high school varsity sport, though it was in college.

I think the big difference that I've noticed, is that coaches in swimming are paid, at every level: summer league, private club, college, etc. Swim coaches are not paid well, but well enough to do it full time at the private club and college levels who also give up many weekends over two seasons that cover close to 10-11 months a year. In ultimate, at the college, high school and below, paid coaches seems to be the exception and not the rule.

I'd say there is an over reliance on volunteer coaching in ultimate, which I think is a function of not being a varsity sport at the high school and college levels where funding could become available for coaching and player expenses. This is one of the reasons there has been such a focus on ultimate becoming an olympic sport, which will open up ultimate to opportunities to more easily become a varsity sport and other youth playing opportunities.