as runway length plays no part in calculating V1
Not quite the case and very misleading without some caveats.
As with most performance limit calculations, the pilot/operator has to ensure that a number of considerations is addressed with the result that one will become the limiting case for the particular set of circumstances - normally we are concerned with determining the maximum weight for the takeoff. Indeed, change the situation a bit and the limiting case may/will change.
In respect of runway length
(a) if the runway is longish compared to the particular aeroplane's needs, it may not become the limiting consideration for figuring a suitable V1. However, it will still be addressed as part of the process to determine the limiting factor as that process usually is addressed as sausage machine calculation.
(b) if the runway is shortish compared to the particular aeroplane's needs, runway length may, quite definitely, become a significant input into the determination of an appropriate V1.