Yes, you can choose, especially in a good economy where you can turn down the crap that you really don't want to do, and there's enough clean work going on to allow you to make a living just from that. Locally, we have a new baseball stadium under construction which will require the talents of thirty licensed plumbers for the next couple of years. Also, all the pipe farms left sitting there by the current depression which started in 2009, they're being finished out as we speak, all over metro Atlanta. Several of the larger plumbing outfits are offering a 2k dollar sign-on bonus for qualified people.
You can pick and choose, but not in small town America. You got to go where the work is sometimes.
I'm scratching stuff off the list more and more as I get older; that being rooting drainpipes, dragging cast iron bathtubs up flights of stairs, and numerous other unpleasantries. Sewage injector pumps are next. I hope.