Not in my case, and I'm more 'experienced' than you are in China - been here before you ever thought of comin here; but unlike you, I've special 'visa' needs..lol! And recruiters assist me greatly to achieve same. As do agents, especially River's company in Yuncheng of Shanxi.
Money ain't everything - I get a massive 'power' kick out of my 'visa' games. Much better than havin loads of money to spend. Please don't generalize in future.

I've heard glowing reports about the agent/recruiter, Yuncheng IELTS. I am told they really value their native born English foreign teachers, not having too many of those.

Yes, I think it adds a bit of zest to life, working on L&F visas; and you can be more flexible. Probably if you are not married it's best that a co-operative school like Yuncheng IELTS to turn your L into an F, because they can renew it in Shanxi Province. As you are married, no sweat, because you can get a year-long spouses L. Good man.