The back and sides are made of the densest, stiffest materials possible (rosewood, ebony, etc) It is their very lack of flexibility (and the lack of movement at the rim) that makes them desirable... The soundboard on the other hand needs to be as flexible as possible. French Polish is beautiful and much thinner and more flexible... but is not very durable or bullet proof
From a user's standpoint, a stiffer, more durable finish on the back and sides is probably more practical... I suppose each luthier has preferences for how they set up their production... (spray versus french polishing or a combination of the two)... even in the "old days", luthiers often used different finishes... more durable oil varnish on the back and sides, and french polish (or an even lighter finish on bare wood for lutes) Many (like me) don't want to deal with toxic chemicals that require humidity controlled spray booths and serious respirators to apply... I have not yet tried any of the water based polyurethane finishes, but have used all french polish, and combinations of oil varnish and French Polish, or lute wax on bare wood.
French polish, oil varnish and lute wax all have visual and tactile qualities that really can't be imitated... so on a very expensive hand finished instrument, that is obviously a consideration as well... (much of the added cost is because these finishes are time consuming to apply and cure properly (hours, versus weeks)