Always Run an Auction
magid.substack.com
magid.substack.com
Classical auctions aren't a good fit because they can't handle non-price factors. However, a combinatorial clock auction could handle non-price factors while also improving price discovery. But as Milgrom says (paraphrased), the best auction is the one people use, so the more realistic outcome is what OP describes: running your own (implicit) auction.
That said, you can think of the auction in two parts - the first gets the relevant people from the starting line to the actual bidding. The second part is where you actually make decisions. The latter part in this dynamic usually has few enough participants that a founder can run the variables in his/her head.
What would be interesting to see is whether or not more funds would get to the bidding stage with a robust combinatorial auction at the beginning of the whole thing.