Traders want deal flow. They also need to trust counter-parties. It really isn't in anyone's interest to have a market participant who mis-prices everything, because they won't be able to both buy and sell (and they will likely soon be out of work). Even pretty dumb traders will quickly realize when it's me, it's not everybody else, whose model is wrong.

Now, it's a whole different story if you are not a trader, for example you run a massive pension fund, a university endowment, a government treasury, etc. In that case, the investment bank's attractive salespeople will invite you to golf at a famous country club, a helicopter tour of the city, dinner at the best steakhouse in town, all while lying through their teeth about the value and safety of the financial product you're about to purchase.

Yes of course. But you have more than one counterparty. And not everything is a thing you're currently considering to trade. You might well use them to calibrate.