First you cannot choose which sport you child will be interested in. I always thought mine would choose swimming but my child chose ice skating. So we do that. Swimming is not a "cheap" activity because you need a facility and those are expensive to maintain. Yes it cheaper than ice skating but everything is relative. Have you ever noticed that for the most part, swimmers come from more affluent families? That should be a good indicator about the expenses involved.
My husband when to college on 4-year scholarship to a Division I school. He once commented that his senior year he spent the night in 26 different hotel rooms (that is ALOT of missed classes). He is very proud he graduated in 4 years without taking summer school - not a lot of 4-year Division I scholarship athletes can say that. He also said that unless we were desperate, he would rather we pay than send our kids on college on one of those scholarships. He was a swimmer - All American and met the Olympic cuts. After he graduated, he did go in a pool for about 10+ years. We met year later at a pool - he was lap swimming and I was teaching swim lessons.
While ice skating may not offer college scholarships, I think ice skating does offer more opportunities to make money than alot of other sports - Disney on Ice and cruise ships want skaters. Long-term skaters have a realistic shot of getting one of those positions (we have known several). Some kids go to college and then the Peace Corps - I see another option as college then Disney on Ice which allows to the skater to travel while earning some money.
Also, you make alot more giving private lessons in ice skating than in swimming. I taught private lesson through the county and I know how much the swimming parents pay compared to how much I pay for ice skating private lessons. Coaching can be made into an income stream during the college years.