I see that you've done your Maths, Bletchleyite, it would indeed take a four-car EMU running every hour to provide the same total capacity as a three-car DMU running (up to) every forty-five minutes.
I think there are three issues here, which aren't necessarily related.
1) Electric v diesel v bi-mode;
2) Forty-five minute service of three-car MUs (with only one train every three hours continuing south of Oxenholme) v hourly service of MUs with every train continuing south of Oxenholme;
3) The balance of trains running to/from Barrow and to/from Windermere.
I don't think the latter idea is in any way dependent on electrification. A four-car 769 or a four-car 195 set (2x 195/0s) would provide the same capacity as a four-car EMU, and, at least over the electrified section, a 769 would provide the same acceleration. A 195 set would come close too, I'm sure.
Passengers travelling locally between Oxenholme and Windermere would be unlikely to welcome the reduction to an hourly service, but the better-than hourly service doesn't currently last all that long anyway, and I don't think people can really complain about an hourly service, given the constraints of the single-line.
On Sunday morning I travelled on the 1241 Manchester Airport to Barrow from Piccadilly to Lancaster, and it certainly didn't almost completely tip out at Preston, in fact I don't think there was much of an overall change at all, the same at Lancaster. On the other hand I have mentioned elsewhere that a majority of the passengers arriving at Preston on the 1933 ex-Airport were terminating their journeys there (or, at least, weren't continuing on the same train) but, while certainly more than half, I wouldn't have said that it was the 'vast' majority who weren't continuing. It's probably heavily dependent upon time of day.
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