I wouldn't replace that plywood but would make it out of G-10 or even koosa. In this way you eliminate the rot problem, which is primarily a problem of builders (like Hunter) and owners painting exterior-grade plywood with fiberglass resin and considering it 'saturated'. If they'd used WEST epoxy, that might have been something; but note that many of our Cherubini-designed Hunters were made before saturation epoxy was a big thing. My dad was the one who introduced WEST epoxy to Hunter as he had been using it to build ultralight-airplane spars.
My H25 rudder comes up through the seat (tiller-only boat) and the corresponding part on mine was bad too. Without even removing the rudder I lifted the old fiberglass plate and screwed it down on 5200. I then went underneath and tabbed the rudder tube to the underside of the seat. The only reason this wasn't done at the factory was in the interests of time. The rudder tube was 'glassed into the hull and the hole cut into the seat (part of the deck) prior to the deck's going on. The fiberglass plate on top of the seat, and the little blocks other people have observed, were added to 'trim off' the imperfect hole chopped into the seat (and my money is on no two boats' holes and plates being exactly alike). A seaworthy boat would definitely have this tabbed-in with only 'glass-- no plywood at all. There should be no opportunity for rot or leaks between the bottom of the rudder tube (in seawater) and the top of it, where either the tiller head or the quadrant goes, which should be as high as possible and heavily supported to the hull. Resolve this and the problem goes away for good.
That said, beefing-up the rudder tube itself with more 'glass, especially tabbing that spreads down onto the hull in all directions, is pretty much a no-brainer if you expect any serious sea time in any originally-cheap production fiberglass boat. My blog shows how I improved this on Diana.
BTW-- use of butyl tape for keeping out water or holding things down is not, by definition, in the interests of making a boat truly seaworthy. Sorry.