Check stays are typically there to limit mast bend from the application of backstay tension. Adding backstay tension is intended to induce some mast bend (to flatten the main) and to also tension the headstay. If the mast bends freely, most of the tension goes into the bend and the rig actually gets shorter (masthead closer to the deck) and all the rigging slacks slightly.
The check stays limit the bend to what you want (if properly set) and allow some transfer of the forces to the headstay.
On our last boat, which used checkstays, we primarily used them upwind for the reasons above. Off the wind we stowed them forward and used the dedicated winches as secondaries for the kite (unless it was nukin', then we set the weather checkstay too)
They are important, and they do pretty much require another crewmember to handle them in a tack, much like running backstays. They are not generally as "crucial" to rig integrity as many running backs can be.
If you get used to using them effectively you'll go much better upwind.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)