Hold on a minute...

Now if barkingcat has a specific objective, as opposed to "seeing Tokyo" he has time to get this done.

I for example fly ANA from BKK to SFO regulary and a stop is not allowed. My inbound arrives at 07:30 and my outbound is at 16:55.

I clear customs and head straight for the city. Meet a friend for lunch and head back with plenty of time to kill in the lounge.

Now if the object is simply to "Visit the Meji Jingu Shrine and walk Omote Sando in Harajuku" "See The Imperial Palace (Although it is not well seen from anywhere)" "Go to Akihabara" "Eat Sushi in Tsukiji" "Graze the food halls at the Department Stores and walk the Ginza and see a Shinkansen while you're at it" "Go to Shinjuku" "Visit Roppongi Hills" "Go to the Top of Tokyo Tower" "Head to Asakusa" or
"Experience Hachiko Crossing in Shibuya" etc.

I would argue that it is doable.

Example:
Land at Noon, Ditch your Bags by 1:00. At NEX and on a train by 1:30.

This is the point where you say "I have 2 hours and 12 minutes of train in front of me and I should be back at Narita by 4:30 for my 6:30 flight."

Hmm...
Maybe it's not such a good idea after all with only 6.5 hours...

But if you had a great reason, wanted to head to the City for possibly just 45 minutes, and still had the ability to do the math on your trip after clearing customs and ditching you bag...

I still say it's doable for a veteran.