I hadn't forgotten about taxi services. But most park and rides relate to commuter flows. Given that a large proportion of rail passenger traffic is commuter flows, relatively few commuters take taxis or hire cars each day at the 'work' end of their journeys.
Indeed, I doubt any city has sufficient taxi capacity for each arriving passenger to take an onward taxi journey. I presume that could be checked quite easily by finding out how many registered hackney carriages there are in a random town (e.g. Reading) vs the passenger usage stats for Reading station. I doubt there's taxi capacity for even a quarter of the arriving passengers if you filled every taxi fully.
Taxis typically carry one passenger onward, whereas a bus can carry 50+. It was a big issue in rail decline post Beeching cuts (1963) that the replacement/interconnecting buses were so poor, and nobody parked-and-rode because they couldn't complete the 'last few miles' at the other end of their train ride. They just drove all the way. Hence I say that the park and ride should allow passengers to drive at the 'origin' end of their journey only. It would (realistically) ensure investment in local bus routes by players or (realistically) lead to a drop in traffic if they are neglected.
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