Of the original three routes, the North (Poulton) and South (Lytham) routes served intermediate stations and the former also the Fleetwood branch. The Central (Marton) route had no intermediate stations so was only ever about providing extra capacity into Blackpool. So when that capacity was no longer needed it made sense to close that one, and I'd guess Beeching's preference was based on some spurious analysis (such as the line with no stations having less costs - please note this is speculation on my part). So this was probably the best outcome for rail passengers, although some ended up a bit further from their destinations in Blackpool. I agree it would have been desirable to retain the short extension from South and a much slimmed-down Central though.
From the council's point of view they wanted to provide for tourists arriving by car, which was done by converting Central station and final approaches to parking and the line that served it into a motorway continuing into the town as a grade-separated highway (it now seems to be unclassified). They couldn't really have done this with North, as the railway was still needed as far as Poulton at the time to connect to the Fleetwood branch.