It's not a better estimate, because it is blatantly an underestimate. Promotions are ubiquitous in chess, multiple promotions are common (even in a tiny sample of a few million games). To suggest you can eliminate multiple promotions in a strategy that deals with way over 10^30 times more positions than the tiny sample of chess that has been seen is not only not proven but also highly unlikely to be true.
Imagine something that is extremely rare in chess, say so rare that there has only ever been one example in the history of chess. Now try to imagine what would be 10 times less likely, Then 10 times less likely than that. Repeat this more than 30 times. That is what you are claiming you know.
You don't.
But regardless of just how well you can avoid multiple underpromotions in an optimal strategy (with careful definitions, there is some minimal degree of underpromotion that you cannot remove while remaining an optimal strategy), the point is that you don't prove anything by waving your hands wildly, which is what you are doing. Proofs need to be thorough.
For example, if you were trying to prove the 4 colour theorem, looked at a million graphs and then used inductive reasoning from those graphs to make a claim about all graphs, how good a proof do you think you would have?
(Hint: not at all).
#809
In the initial position white is a tempo up, that is an advantage, hence white tries to win and black tries to draw.
If a sequence of moves leads to a draw, then that retroactively validates all black moves: they were good enough to achieve the goal: to draw.
On the other hand if the sequence of moves leads to a draw, then it might be that white somewhere missed a winning move. Hence all white moves need validation by examining takebacks.
Multiple promotions are rare. 1-2 promotions per game are common, but 10 promotions as in the first Tromp sample position not.
Excess promotions are rare. Usually a pawn promotes to a piece already taken. 2 excess promotions usually to a 3rd and a 4th queen happen but rarely. 10 excess promotions never happen.
Underpromotions are rare. When a pawn promotes, then it is in 99.9% of cases to a queen. In rare cases it is a knight, e.g. to promote with check. In rare cases it is to a rook or to a bishop, to avoid stalemate. 10 underpromotions never happen.
10 excess underpromotions never happen, that is why the random sampled positions as counted by Tromp play no role in solving chess and why thus the Gourion number 10^37 is a better estimate than the Tromp number to assess the feasibility of solving chess.