sfmans,
"(a) the design of the instrument includes rests for the 4th fingers"

RE:The rests were intended for 4th AND 3rd fingers and this is obvious from their design and location. Anyone trying to use them for 4th finger only must find that the location is faulty and the comfort miserable

.."suggesting that the little finger is to be primarily employed in bearing some of the weight of the instrument"

RE: One may think so! but the rest is so obviously dysfunctional for that purpose that it is astonishing it has survived for 150 years

"(b) the fact that most beginners' tutorials teach people to play with three fingers"

RE: This misfortunate advice certainly is important along with the fact that so many players of the English have started on their own and no established and systematic pedagogy has ever been available

"one of those rules that is great for beginners but limiting for adepts"

RE: Here is the clue I think - but mostly on the contrary as I see it!
Whatever skill one is learning it is important learning the most efficient, comfortable and developable methods from the start.It does happen that a "beginners way" may be a shortcut but often turns to the opposite and in THIS case there are very good grounds meaning that: 1) the finger rest itself is contraindicated 2) liberating all four fingers for keyboard work is preferrable - and starting off in a way that better be rejected later is wasted effort

So - why not take the consequences once and for ever? Four fingers and NO finger rests ! C Wheatstone no doubt was a great innovator but here an unfortunate mistake was made that has misguided generations of concertina players.It may be difficult for 'us' to change our bad habits but consider the poor posterity...:-)