Been where you are, and managed to move from that hobby state to selling and making money. I made the move for the exact same reason you indicate - expensive hobby. That said, 6 years later I now shoot professional sports, and have a successful T&I business.
My first few years were not about making a profit, rather learning, growing and buying more gear, without dipping into personal money.
Many responders have indicated the pitfalls you will have trying to sell prints online. And I have to agree. In today's world, very few people want "action" prints. They do want the Posed T&I when teh kids are young, but for action they only want digital files they can share.
For the longest time I would bring my camera to my son's games and take photos, other parents would ask for photos and I would give them a CD. It was a lot of effort, and while they appreciated it, it got to the point where if I didn't have my camera at a key game, parents would be disappointed that I wasn't taking photos to give them.
When I started to do T&I, I also found those same teams my son played on expected me to do our team for free, when I gave the manager order forms to hand out, some parents were upset I would charge them. Still it was a short term pain with just those teams, and by the next season they realized they weren't getting free photos.
For Action photos I will come out and shoot action of a game, but it is at a flat rate booked in advance. Since you can be almost guaranteed that no one will pay for photos afterwards. On several occasions I was shooting sporting events for one team, and parents from the other team would come up and ask if I was shooting their team, and I would tell them I was hired by the other team. They would ask if I could get photos of their son/daughter they would buy them. I would tell them the rate I charge per photo, and they would be yes that is reasonable. I would take their email address, During the game I would shoot a few of their kid, and put them up and send them a link to my online store to buy them. In 6 years, I have never had a single one of those parents actually buy a photo of their kid.
In short, as others have said, you can make money doing T&I, and while you may not like posed shots, that is where you will make your money. If you want to offer a package, T&I and a CD of Action, do that. but it is the T&I they are really paying for. If you hate posed shots for T&I be creative, set it up that the player skates around the net and you take the shot as they come around, or they kick the soccer ball, and you take the shot as they make contact. Don't want to deal with prints for T&I only sell a digital package.
Probably not what you were hoping to hear, but it is the sad truth in many places.
good luck with whatever you decide to do.