You can ride a flat bar bike farther than 20 miles. I have a flat bar road bike, and a drop bar road bike, and find little to no comfort difference. Most of my rides are longer than 50 miles, and the flat bar bike is the most often ridden (it used to be my only bike, now with fenders it sees more weather related ride time).

If you take the time to figure out what makes a flat bar comfortable, they are fine. By the same token, I have a cheap flat bar single speed that is incredibly uncomfortable after 10 miles and needs attention. I haven't decided yet whether I will do drops or flats, but I am certain that I can make either option work fine.

That being said, I am not recommending the trek FX. Do whatever you want. If you want carbon, good luck. If you are a big guy, my experience has been that entry level carbon stinks for big folk, because it feels like a noodle. YMMV.