I briefly considered something like this, but it didn't seem worth it to me. I don't have outside space to compost, but I do have a garbage disposal and generate much more recycling than trash. We generally put out one bag of trash every two weeks and our 20 gal can accommodates about 2.5 tall trash bags.
I happen to live less than 1 mile from a garbage transfer station. It costs $20 to dump at the transfer station, but my tiny trash can costs $10 a month. So I'd have to go at least three months between paid dumps or find a dumpster I can use weekly for one bag without getting in trouble. Ultimately, I just decided it wasn't worth my time, but it could have saved $40-120 a year. I like the idea that it keeps you more honest with yourself about how much trash you generate when you must be disciplined about it. Reducing trash is always a good idea.
If you think it's worth it, go for it. I just reviewed the waste management site and realized I can get a monthly trash pickup for $7, rather than weekly. I didn't realize this was an option, so thanks for the reminder to check the website!