I remember the compartment stock on the Southern Region, and I quite liked the old 4-SUBs where, in quieter periods, one could have a whole compartment to oneself, nice and quiet, and sit and read or just look out of the window. With other stock, there would be compartments with a side corridor; again, that was a nice way to travel. It's fun to travel on, say, the Bluebell Railway where many of the carriages are like this.
But the days of having such stock on national railway lines are long gone. Other people here have noted accessibility problems and security problems. There's also structural matters: how would compartment stock, whether individual or corridor-linked, manage with the wide sliding doors necessary on commuter services? Open carriages, perhaps with some floor-to-ceiling semi-partitions that do not protrude into the aisle, are the present and future.
Also, the trend seems to be further away from any vestigial 'compartmentalisation' towards longitudinal bench seats with a very wide aisle: the stock on the Euston to Watford, and North and East London Lines are all like that, and whilst for enthusiasts like us it's a right pain not being able easily to look out of the windows (not least at interesting points such as Harlesden and Stewarts Lane), it suits these lines as large numbers of passengers can be carried and can swiftly board and alight.