The reason Short Back, Inventor and Pate are all joined together, with the credits taken out, dates back to the original BBC Video release back in 1984.
BBC comedy programmes became available to buy on video for the first time in 1983 and 1984.
The first programmes to make it onto BBC Video included The Fall and Rise of Reginald Perrin, The Good Life, Butterflies, Fawlty Towers, The Goodies, Open All Hours and Last of the Summer Wine.
On these early videos, for some unknown reason, these programmes were often 'top and tailed', joining two or three episodes together, removing the intermediate titles, and making a new set of closing credits, combining all the credits from all the relevent episodes.
In the case of Reginald Perrin, seven half hour episodes were condensed into a two hour adaptation.
That's what they did in those days, you would rarely get a complete series of anything. Nowadays a whole series is released the day after it is shown on TV.
Anyhow, this 1984 Last of the Summer Wine BBC video, featuring the first three episodes from Series One, in this edited format, was re-released in 1990 as a WH Smith exclusive video, in similar packaging. This release also had the episodes edited, as before.
(The artwork on this single BBC Video box was quite stunning: it was a photograph of a cobwebby wine bottle, with Clegg, Compo and Blamire, and a fantastic view of Holmfirth, on the bottle label.)
In 1991 the remaining episodes of Series One were released as three full episodes.
In 1993 a double VHS video was released featuring two tapes called The Complete Last of the Summer Wine Series One. The tapes were exactly the same - the first tape had the first three episodes edited, the second tape had the remaining episodes as three full episodes.
And then in 2002, Playback released exactly the same content on both VHS and DVD.
So that ridiculous bit of adapting done in 1984 has remained ever since on video and DVD - no company in the UK has changed it (as far as I know, don't know about the latest DVDs). Can't speak for US versions.