I can't believe anyone would make such an assumption. I know some people who 1) voted leave 2) are perfectly aware that under WTO rules their businesses would literally have to close because they trade with EU and their European partners won't accept a ~20% hike on the price of British products due to non-EU custom duties. They all wanted out of EU because they don't like the immigrants, because they think Brussels has too much power, but they all wanted easy trade with the EU. WTO trade is not what they voted for.
There isn't a single one reason why people voted leave.
Trade without agreements is subject to tariffs and major restrictions severe enough to cause serious economic damage.
Agreeing FTAs can take years, hence the need for a transition period until one is agreed between UK & EU.
What May did was entirely consistent with trying to achieve the Brexit that was voted for.