USA has free trade agreements with many small countries as well as large economic areas. They have demonstrated very well how this can be achieved. A small country in relative terms is Korea and they have a thorough free trade deal with USA.
Nobody said they didn't. But did they demonstrate anything favourable? It took the best past part of a decade to agree that FTA, after a twenty year hiatus, and it's not there yet still. America wasn't in a particular rush to sign either, and got the better side of the terms!
But you've obviosly read the deal itself, yes, and you knew how long it took to get the opposition in the US to making new FTAs down, in the first place? Here:
https://ustr.gov/trade-agreements/free-trade-agreements/korus-fta; you can count them (who is a more proactive trade bloc in approaching other nations? It's not the US) for Korea the wiki entry for this is being fought over, so go straight to the sources at the end:
https://en.wikipedia.org/wiki/Free_...d_States_of_America_and_the_Republic_of_Korea.
In fact, the Office of the USTR lists all major US FTAs. Tell me, are the smaller economies winners? Does America offer a better market than the EU?
Why should we choose to approach them from a position of weakness?
What's the point of leaving, if the EU either already has agreements with the major markets we are interested in, or is in the process of negotiating access to them; this includes the US, Japan, China, India, Russia, etc?
Why not leverage the EU to get the deals we want, whilst remaining a member of the largest free trade bloc?
The EU offers greater pooled negotiating power, a healthy economic buffer and a system of checks and balances to counter the biggest of players like China and the US. How would you get any of that independently? EEA? Think again.