With turbotax online, you can prepare up to 5 state returns and e-file all 5. If you have more than 5 states, you must use the desktop version.
The desktop version of Turbotax can load and prepare an unlimited number of state tax returns, but only 3 can be e-filed. The rest have to be printed and mailed in. This is a security precaution because, 2 years ago, there was a dramatic increase in fraudulent tax returns by people who e-filed many bogus state returns, taking advantage of the states' weaker security.
I'm not sure why you consider printing and mailing the state returns to be such a hassle that you will change companies over it, and I suspect (but have not tested) that other companies will have the same security restrictions. Good luck.
https://ttlc.intuit.com/questions/1899266-how-many-state-returns-can-i-prepare-in-the-turbotax-cd-do...
