I made an offer to a seller with that feature turned on at the starting bid price, and he rejected it. The auction is still live, with no bids, so let's see if I'm still interested when the auction closes in a couple days.
Separately, an item was listed yesterday with a starting bid of $150 or best offer. I saw it and immediately offered $200, which the seller accepted. I was fine with that price. Maybe I could have just bid and won for $150 a week later but I didn't want to risk it.
Conclusion: I like that bid or best offer feature. I think I just like having options as a buyer.