What I really do think they'd need to explain, better than tried here, is how being an Olympic sport would be good for the rank and file, because while saying "Skating [nineteen years ago] had five-figure purses [before taxes and who gets to keep what depends on the fed, and to get within a remote shot at winning said purses you/your parents have already spent probably half a million dollars AT LEAST] which would be good for dancers to have a chance at winning" sounds kind of nice for them, setting aside the cost-benefit (again, I worked in one of the elite skating clubs, I saw parents and what they were spending and what kids had to do to be considered competitive at levels like Novice, where they're 13 or so, and we're talking second mortgages, splitting families, commuting to Boston weekly from ALBANY to get the 'right' coaches, and of all those kids? ONE I know is still competing at an elite level with a reasonable shot at potentially getting on a World or Olympic team someday, while most never got even close to that far, washing out long before) there are other issues. $30,000 only sounds like a lot of money when even getting a one in twelve chance at it hasn't cost you more than some people make in ten years of work.
And that is ONLY for the kids who start young and have some faint hope of getting into the top narrow tier of athletes in the sport. USFS is a federation focused on, ultimately, cultivating elite competition. Trying to attract people other than little kids, who will then be weeded out as learning levels get harder and harder (the test stream is designed to narrow the field down-if you can't pass, you can't compete at that level, and if you repeatedly can't pass, you're being sent a message) is a very low priority. The people who make coaches big money are the ones who still have a chance at competing in the 'serious' events who are taking lessons five days a week. (And if you're only taking one, it's still $120+/hour for those coaches.) The Adult test track and adult events are low priority, even when the fed pays lip service--Adult Nationals is basically a sideshow, and there's no true, qualifiers-only Adult Worlds related to AN. Adult skaters are not going to get to the Olympics, so it doesn't make sense for the fed to devote much time and resource to them.
As for the "sponsorship!" thing....um, I am willing to bet if you asked people who they think have gotten big sponsors and endorsements in skating, they're going to start naming names like...Dorothy Hamill, Peggy Fleming, Brian Boitano, Nancy Kerrigan, Kritisi Yamaguchi, Tara Lipinski, Michelle Kwan...only two of whom aren't Olympic gold medalists (Kwan has a silver and a bronze but is the most decorated US Ladies' skater of all time otherwise, Kerrigan has a silver and is mostly famous because of the famous whack on the knee) and none off whom have competed meaningfully since 2006. The sponsorships in the US have always been largely tied to ladies' singles, and we haven't won that since 2002 at the Olympics, and haven't had a medal at worlds until 2016 in YEARS. In other disciplines it just isn't a big seller in the US ever, and even Davis and White becoming the first Americans to win the ice dance gold has not parlayed itself into anything like the fame of a Fleming or a Kwan. Skating is in fact now in a position of being one of the sports that has to defend the sport aspect every time--sparkly costumes, emoting to music, and going from a visibly-corrupt judging system to an invisibly-corrupt, extremely complicated system, all make skating less marketable. There is a trend/preference to show athletes as athletes, including there no longer being quite the resistance to showing female athletes as physical, sweaty, etc. that there used to be. Now there's a resistance to 'twinkly little outfits', a backlash against perceived sexism in the image of the 'ice princess' and the male/female dynamic of pairs skating, the uncomfortably-young age of some skaters, the focus on aesthetic fitness rather than athletic fitness (one thing that's still true, if you skate better at 105 but look better at 100, the coach wants you at 100)...dance doubles down on almost all of these. It looks even less like a sport than skating by current marketing standards.
And as for exposure...right now, thanks to DWTS, SYTYCD, and other reality shows, ironically ballroom has more media exposure than any skating. Unless it's an Olympic year, competition coverage in the US is delayed by days or weeks and usually relegated to weekend afternoons. There is little to no professional market (and none outside Disney on Ice if you're not a name headliner.) If you're in Japan or Korea, sure, skating can still make you a media sensation, with the good and bad aspects of that (fan wars get UGLY there), but in the US, skaters are going on hokey dance shows for publicity, and most of the ones who've been asked are the ones I mentioned-they won medals when I was in grade school. Or before I was born. And I'm 38 next month. I would not look to skating as some sort of role model.