Yes people have and do. I would never. The towns around our gym are very nice but my husband and Is life and jobs are here so it would never be an option to move. Droplet just turned 9 and could decide to hate cheer tomorrow. You just never know!
Given the option between a forever-long commute and a MOVE to be near a gym, I'd almost ALWAYS advise parents to go with the commute for the above reason and more:
1. Unless your job is one of those where you can quit and literally find a new one the same day, your source of income > cheer.
2. A move for your cheer kid means a move for EVERYONE. Is it REALLY fair (for example) for you to move 16-year-old Billy to a new school in Plano during junior year of HS to cut out J5 Suzie's 3 hour commute to CA?
3. ANYTHING can happen. Seriously. Like you said, you could move 3 hours away to be closer to said gym, your child could get injured, mental block, and be out of cheer entirely for a season or even two. Now you have a home in a town that you ONLY moved to for an activity your kid no longer participates in for the year.
4. This gym might fit your needs NOW, but may not in the future. This is especially true for younger kids. J3 at Super Awesome Elite that is 4 hours away each way is amazing and won NCA. So you move there. She stays there for 2 seasons, you're ready for L5 and said gym decides that they are NOT fielding any Worlds Level 5 teams. Ruh roh Scooby.
5. Another big thing that changes and tends to change things for kids: Staff. You may have LOVED all the coaches at Super Far Elite when your daughter was Level 1-4 but they change staff for all of L5 teams and you find that you're dealing with style changes that you are not happy with. If you moved to be there, you put yourself in a bad spot unless there are other programs around.
6. Things happen. Kids get boyfriends and stuff and decide they don't want to be bothered with cheer anymore. Kids burn out. They change their minds. Even highly-dedicated L5 Worlds team kids quit cheer every year because they're just TIRED. People tend to assume that their Suzy is immune to burn out but no one's is. It's not a fun place to be when you've relocated for something and Suzy comes home and says she is "not doing this anymore and you can't make me." Now she feels obligated because well, you moved for it.
7. Moving generally sucks. For those of you who have not done it recently. It sucks. It's expensive and kids are far from friends from home. Your kid may LOVE cheering at Far Away Elite, but (for example) HATE her new school in Far Away town and come home miserable every day because she misses her school friends. Is that worth it?
8. Do YOU as an adult really want to rearrange and relocate for your kid's cheer life. Ex: You have BFFs from college, church home group and bible study that you've been part of for 10 years, and other relationships in life that took years to build. Are you willing to (as an adult) move to a new town and develop new friendships based on your kid's activities?
This is not to say that you should NEVER move for cheer if you're cheering somewhere that is ridiculously far. It's just important to consider your entire family and other factors, not just cheer in a vacuum.
I've known some "moved for cheer/dance" families and it is not to be done without a lot of thinking.