That's true for public projects as well.
Often the client will be happy to get a cheap offer, only to be surprised that the project is delayed, requirements are not met and there are huge follow-up costs.
And then sometimes all sides know that the project can't be done for what the lowest bidder offers and the whole bidding process has to be done again with restrictions that prevent the cheapest bidder from applying again.
Lowest-bid mechanisms sound great in theory, but absolutely don't work out practically and we all pay the price for it by getting a bad return on our tax money. On top of that, the system doesn't even prevent corrupt politicians from funneling government jobs to their friends.
Then again, good luck finding a better system.