Personally, I'm not concerned with fuel theft. Have yet to be a victim of that crime in 48 years so no locking cap or door for me. If I find the filler opening getting packed with ice or snow this winter I'll re-evaluate the need for a filler door. Otherwise, I'm going au natural.
I really like the look of the exposed fuel filler cap but I can see concern that someone may steel that and/or put something in your tank that doesn't belong. I might add a locking fuel cap but the door spoils the look.
The comment about snow building up does make sense and that would be the only reason I would add one.
I don't worry about theft from the fuel filler port/cap/doors. I was pretty sure all vehicles made in the US have to have that rollover fuel check valve thing. Most of those make it near impossible to siphon a tank. ETA- obviously it does nothing to prevent a dirtball from adding something to your tank.
Now the shitbirds that punch a hole in your tank to get your gas and leave the rest of it to leak on the gound, well they deserve a shorter lifespan. I've heard of a couple of those in the last 5 years.