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> Under what circumstances would you possibly be able to exclude it?

When I have run the test games with an engine that does take full account of the mating potential or lack thereof. Then there would be no reason why pieces with mating potential would be under-estimated compared to pieces without it, as the engine would not miss any tactical shots that secure a draw by exploiting such lack of mating potential, and would also resist putting itself in a position where the opponent can pull such a trick (e.g. like trading from KNPPKNP into KNPKN, so the opponent gets handed a NxP sacrifice as an easy drawing strategy).

Spartacus should be able to do this: it recognizes drawish material combinations, and will reduce the evaluation by a factor if the naive additive evaluation says the side with such material has the advantage. In particular this applies when the leading side has no Pawns, and is not more than a minor ahead, (reduced by a factor 8), and positions with a single Pawn where the opponent would not more than a minor behind when he sacrifices his weakest piece for that Pawn (reduced by a factor 4). Unlike color-binding of the last piece on both sides also gets a reduction (by 2).

The concept of 'minor' deserves some attention here: strictly speaking a minor is defined as a piece without mating potential, but most Chess players think about it as a piece with the value of about a Knight, as in orthodox Chess that amounts to the same thing. But there are pieces that in my tests perform like a Knight or even slightly weaker, despite the fact they have mating potential. (E.g. Commoner (FW), and Woody Rook (WD); even Gold (WfF), a subset of the Commoner, has mating potential on 8x8!) This makes the rule-of-thumb of 1 minor ahead a bit tricky: WD + N vs WD is only a Knight ahead, incontestably a minor, but it is a general win, as the stronger side can use his superiority to force the trade of N vs WD, to be left with a winning WD. The mating potential has no special advantage for the defender. With R + N vs R the defending R is too strong for the N to get a grip on it, and the only trade that can be forced is R vs R, which makes it a draw.

So the rule seems to be that the stronger side can force a trade of his choice of an approximately equal piece, but the weak side can make a sacrifice of his choice (so that 2B+N vs R is a win, but in B+2N vs R the R goes for the B, making it a draw).