I'm not pointing out that Ace is mad because I'm trying to say he wasn't thinking straight. I'm pointing out how mad Ace is because that emphasizes how strong his desire to kill Teach was. Which means if Ace had Haki at his disposal, he would have used it, regardless of whether he knew Teach was a Logia or not. The notion that Ace wanted to test whether or not Teach was lying doesn't make sense because, regardless of whether or not Teach is a Logia, why NOT use Haki? Why NOT use something that enhances your abilities, especially when he tanked one of your strongest and signature technique, regardless of whether or not they are a Logia? By this logic, why would anyone use Haki unless it's against just Logias?
You're pointing out how mad Ace is to justify your thought because you believe someone angry is out for blood off the bat but that's just your pov and it's applying real life logic to a comic. Almost all comic fights start with a building up phase, it doesn't follow real life logic but it's consistent in comics so you acting like it's impossible for a comic author to not consider real life emotions and draw a standard comic fight is beyond stubborn. Also the author knew Ace had to lose for the sake of his story. If you wanna play the why didn't they card, why didn't shanks a known and accepted haki user and beast lose his arm? Simple answer is because Oda was choosing a time to reveal this information. And the "I bet it on the new gen." answer he put in the manga is an escape answer we have to accept because really he could have used conq. to run it away like he did after losing the arm or used armament to keep it but at the time the story needed him to lose it the way it needed Ace to lose.
That fight didn't really last long either, and most of us accept that BB despite his character is actually strong, he managed to damage Shanks pre-fruit. So Clearly he was above Ace at that point then on top of that he had a new DF that negated Ace's powers which he didn't learn until it was too late. The fight wasn't that eventful either; Van Augur and Burgess attack, Ace uses Fire Fist and hits teach, he rolls around for awhile, gets up and shows black hole, Ace uses Firefly while he's talking, When BB gets up he explains his fruit some more and uses Black Vortex, from the point Ace learned he wouldn't have his DF BB hit him with a big punch that left him reeling and winded and this is from a guy we've established was strong enough to hurt Shanks so it absolutely took a toll on Ace, after getting up he's pulled again and uses a fire attack on his way in, it's at this point I know you'll want to ask why not use haki here and to that I refer you to my part below, Ace's haki fists may still have not been as strong as his DF skills if he hadn't had much training with it at that point. It plays with a typical build up scenario only this tiem around Ace didn't get a chance to go through his full cycle because BB outclassed him as an opponent in strength and w/o his intangibility he couldn't defend against BB.
To your point about why not use something that enhances your abilities, that's all speculation, perhaps his haki wasn't far along enough to coat his fire attacks and his haki fists are still not as good a fighting method for him as his DF techs. And Logia are one of the only time you
need to use haki that and fighting another haki user. Luffy doesn't go around using haki on opponents that don't need it just because it would be easier or he could have used it all throughout the Colosseum. Just because it makes sense in a real life situation doesn't mean the author will think of it when they're writing.
Lastly I've been going back through the chapters related to the issue and did it say Ace was going to kill BB, I know he went after him on his own and as you said he was angry and wanted to kill him but WB is their captain and as a pirate the captain is judge and jury and executioner WB even said it was his responsibility to teach BB for killing Thatch so isn't it possible Ace was there to bring Teach back to WB for punishment? Unless it's said he went to kill him personally. I went back through the fight and the meeting between Shanks and WB and Teach is the only one who says" I know you want to kill me" Ace says"You know why I'm here" but those don't equate to the same thing, Ace could have been there to take him back to face WB's justice just as easily as he could have been there to kill him himself.