The biggest issue is that'd take a really really long time. The amount of dV you get out of a solar sail is minuscule at scales that will work well in the neighborhood of Earth.
Oh, absolutely - solar sails in general only really work for things like satellites and probes (and, possibly, asteroids) where you can afford to give them quite a while to get into place, so no manned solar boats here. Although you can do some interesting things with them in gravity wells (statites, anyone?).
Still, you only need to perturb your orbital plane a very tiny bit to be out of the way of future launches, and then you have all the time in the world to navigate to where you want to go.
Yeah the months to years it would take depending on the payload and size of the change though would be pretty costly for the businesses. I think a more likely solution would be having a handful of launch loops on common inclinations and anyone requiring a very specific inclination launching with a booster attached to take care of it. Depending on how high these loops could launch using the Moon to change inclinations might work. I think more likely though is that basically everyone would find ways to make do with the handful of standard inclinations that there were launch loops for.
