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.
Indeed. I read that the Kemp Town branch was partially conceived buy the LB&SCR to block an anticipated incursion into Brighton by the South Eastern. It struggled on as a goods depot into the 70's.
There was the proposed Ouse Valley Railway in Sussex - this would have passed through very few large settlements. Would travel from Balcombe to near Bexhill through all the little Sussex villages & was proposed solely to keep the rival South Eastern Railway out of LBSCR territory. Construction started but was never finished.
The Brighton Mainline between Earlswood & Purley is interesting. The original route through Merstham & Redhill was shared between the LBSCR & SER (with each company owning different bits). They got increasingly fed up with each other sharing the track and the ensuing service congestion so in 1899 the LBSCR opened the Quarry Line: It pretty much mirrored the original route but had no stations. Built purely to allow LBSCR trains to avoid Redhill & the track-sharing with the SER.
Of all routes built for ridiculous reasons, the Quarry line must have turned out to be one of the most useful.