That actually is the extended cab model. I have a 2000 F-150 4x4 with the extended cab and useful 6-1/2 foot narrow bed. Agree 100% about the 4 door trucks and 4'-5' beds. They're trucks in name only.
Maybe that stock web picture I posted is not very good. What you cannot see is that it has two little doors. It is not even obvious that they are there or that they open. I will attach a couple of actual photos just taken of my 2008 F150. One with the little door open. The cab is not long enough for even a child to be back there. It has 2 regular size doors, with up-down windows and two small doors with small fixed position windows. The regular sized door have hinges at the mirror, just like, almost, all cars. However, the 2 small doors where the storage is located has its hinges at the rear of the cab. Also, it has no obvious handle for opening these doors. One first opens the regular size door and then the handle for opening the small door is exposed just below the small door window. I don't think they ever called this an extended cab. You can see the small doors did not add much to the length as the hinge is right at the back of the cab. See photo.
The bed is a full 8'-1" long and the width between wheel humps is > 48" . So a full 4x8 sheet fits. I used to have a cloth cover that snapped on, but it got destroyed. With that cover on I could haul all sorts of stuff without worry that someone was going to see in and steal it. I tried to purchase new cover, but had difficulty finding one that would actually fit and keep the water out. I purchase the truck in 2011 with 20K on it. I don't use it much any more except for hauling a few things. It now has 45K on it. So I guess I put on 25K in 12 years!
Anyway, I have looked for a new model/brand with the same door and bed features several times without luck.
@pontiac428 I do not see this model in the pictures you put up.A new pickup truck is really just a minivan with a doorless trunk.