It's not at all true that the only goal of a T&M consultancy is to maximize T for any given customer. When you do that, you burn customers, and most consultancies (at least, the ones whose names aren't lit up on the sides of buildings) are extremely dependent on word of mouth and referrals for business.
The normal problem here is simple: the bread and butter of a lot of consultancies are a small set of big "house accounts", where both the consultancy and the client are on the same page about the value being generated and the price tag assigned to it. That's as it should be! Nobody is "full of shit" just because one client puts a 10x price tag on work you feel should be valued at 1x.
That doesn't make WebAgency OK. They mismanaged the engagement --- they shouldn't have done it at all, because they don't have the project management or the engagement structure to do a good job for 1x clients. When they realized they couldn't deliver a satisfactory project for the 1x client, they should either have terminated the engagement and refunded the payments to date, or finished it gratis and eaten the cost; the vendor should, in most circumstances, own the delivery risk.†
But for a lot of clients, and, importantly, disproportionately the clients a consultancy should want to serve, this whole saga is meaningless. The dollar amounts involved aren't high enough to micromanage, and all they care about is the outcome. It's of course still possible to burn those house accounts --- but burning a house account is a very big deal and well-run consultancies will freak out if it's happening.
This is a live-and-learn situation for everyone involved. If you're set up to deliver agency work to 1,000 person clients, you need to be very wary of picking up gigs from tiny sole-proprietor clients, because even when you get into things with the best intentions --- and I take 'mtlynch at their word that that's exactly what happened --- circumstances can fuck everything up, and a small client is going to feel that fuckup in ways an ordinary client won't.
I think 'mtlynch has exactly the right takeaway from this: if you're a small shop, you probably want to err on the side of engaging other small shops for consulting work, rather than agencies, unless that agency can really convince you that they've done the work to rig their business for delivering to small clients.
† Here it's tricky, because WebAgency was screwing up due to turnover and increased workload from their real clients, so delivering the work gratis would have impacted house accounts, and nobody is going to let that happen; meanwhile, 'mtlynch doesn't want them to cut bait and give him his money back, so both sides are limping along in an unproductive stalemate. It's a thing that happens!