I always find it amusing that we gained not one, but two railways (Epsom Downs and Tattenham Corner) primarily to cater for race goers !
The happy ending to this story is that both routes are still with us.
I did read a rumour once that the Catford Loop was built partly because Queen Victoria didn't like travelling through Penge Tunnel. I strongly suspect that this is apocryphal.
The Chatham Central branch over the Medway wasn't unusual in being built by the South Eastern Railway purely to compete with the London Chatham and Dover Railway. The fact that it only ever got as far as Rochester makes it somewhat more preposterous. Nevertheless, the chunky looking bridge over the Medway that came with it is still proving useful to this day.
The OP would seem to mention, at least by implication, such "blocking lines" created to keep the competing company B out of company A's envisaged territory; as a fairly widespread general oddity of the pre-Grouping era -- with OP seeking instances of railways created for yet dafter reasons / non-reasons.
That said -- some "blocking lines" were wonderfully ludicrous, and of rather doubtful use in the role of public carriers. One of my favourite examples of such, is the Great Northern Railway of Ireland's Armagh -- Keady -- Castleblayney branch; which came on the scene very late (opened circa 1910, if I have things rightly); and owed its inception and existence, largely to the GNR(I)'s wishing to thwart perceived plans by the Midland Great Western Railway to "muscle in on" Great Northern territory by extending north from Kingscourt. The southern section of this line, Keady -- Castleblayney, had an extremely brief working life. This was so, largely because of politics taking a hand. At the partitioning of Ireland -- in 1920 or '21, I forget which -- this section (running essentially through [beautiful] "wilderness", generating little traffic) was cut by the new border. The GNR(I) -- afflicted at Partition, by a very large number of intersections of its system by the border -- was glad of the chance to rid itself of one of these anyway, by abandoning Keady to Castleblayney as early as 1922. The section of the branch within N.I., Armagh -- Keady, continued to carry passengers until 1933, and freight right up to 1957, when its connecting secondary-main line through Armagh was abandoned.