I used to work in a furniture restoration shop, where I was "the expert" on chair-seat reweaving. This included both types of caning (hand-woven and sheet-cane) rush (natural cattail and kraft paper) reed (which is the same matierial used in hand caning) and splint (natural wood and kraft paper).
Granted, the cane seat of a chair is subjected to stresses which differ greatly from the seats of canoes. Really big people rarely plunk themselves down on canoe seats, and if kids jump up and down on them, they maybe learn a lesson when they end up in the water. And dining room furniture never spends the winter in a shed or is left lying in the grass. But I will comment on what I know, and what I believe.
It was always my feeling that cane essentially comes with a nice finish on the top, and adding a varnish-type coat just gummed things up. Sometimes a chair was dip-stripped to remove paint, and the cane seat was intact, but the shiny surface area had been lost... or a new seat was placed on a chair with an intact cane back and the new cane had to be stained to match. In those cases, I'd use varnish-- can't recall what type, but probably urethane. (I'm speaking of something that went on so long ago it seems another lifetime).
I removed many-a-sheetcane-seat that was cemented with varnish to the wood of the chair--- I agree, it's a pain! Replacing this sort of seat can be more difficult than weaving a hand-caned one, and it can be hard to predict the difficulty involved in removing old spline until you get into it. There are glues that seem to make the spline become part of the chair.
I believe, when it came to the use cane, back in "the olden days", the surface was probably left alone. People simply had the seats replaced when they went bad-- it was probably easy to find someone to do the job cheaply, if no one in the family could do it. To me, it seems most practical to replace seats with an eye to making it easy to replace them again, as needed... and figuring on doing it yourself.
There's an interesting seat on page 34 of Stelmok and Thurlow's "The Wood and Canvas Canoe". It appears to be a rush seat--- rush is "wide binder cane"-- the same material used in the final finishing step of the traditional hand caning process (which is sometimes left off of canoe seats). This rush seat (which is on an early Gerrish in the picture) would be very sturdy and comfortable-- there would essentially be two layers of seating material, with space between them equal to the size of the seat frame (nice cushiony air-space). Rush seats have plenty of "give". Seems to me this would be a nice seat to put into a canoe, if I were building one from scratch. Perhaps this seat never caught on because it was easier to replace caning... and then the cane seats became "the look" for canoes.