And if your choice is between negotiating a deal with a market of 60m and a deal with a market of 300m, well do the math.
This is a little simplistic. I mean, would you rather have the EU as a market, or USA? EU has something like 20% more people, however, that includes a lot of relatively poor people like Romanians, Polish, etc. I would have thought (citation needed) that the net spending power of USA consumers is higher than the net spending power of the EU.

Of course, if we talk about China, India and Brazil, this point is completely irrelevant. EU is much richer than these countries. But you can't just point to population as though that's all that matters. How much these people spend on imports is very important.

@ bolded. We just voted for more red tape voluntarily. Doesn't make us look like a great trading partner does it.
We didn't vote for more red tape. This shouldn't be the case. If it is, we're doing something very wrong. The EU is notoriously bureaucratic, understanding and abiding by EU regulations requires significant time and investment for companies that want to trade with EU partners. More so now, which isn't a surprise when it comes to the EU because we still have to deal with their red tape , as well as ours, but when it comes to non-EU markets, it really shouldn't be worse than it was. Less regulations, which comes down to the details of the trade agreements. USA in particular should be in favour of less regulations, with them being highly capitalist.