Funny: Sometime after paying off the first time, I was talking with a CSR at one of the credit card companies, and she looked at my account, and said, kinda awkwardly and with surprise, "You've been a very profitable customer...". I'm pretty sure that's not in any script. :) But I did have a stellar credit score by then.
One of my businesses did some great and beneficial work that I feel really good about, but I should've used angel/seed investors from the start. That would've made things a lot less painful, helped me formulate a more profitable business, and helped the second business actually get all the way to launch before I couldn't stomach any more fistfuls of personal debt.
How I see it now: no matter how much I'd prefer to focus solely on product and engineering, and not having to play business-person with investors, investors are so much more preferable to self-funding a startup as a non-wealthy person. If you can't convince investors, I'd advise being very skeptical of a survivor bias story from Airbnb, and instead find a way to modify or explain the business to convince investors. (You could just tell them: "we'll make money by disregarding existing regulations for a market, undercutting the competition." :)