You last point is key and requires an answer to the question: How cold outside are you looking to overcome and actually swim in? For me, in NJ, there's NO WAY I want to go swimming in my pool when it's below 75, much less when it's below 50. For MY needs (and mine alone), I would never use a heat pump to heat my pool when it was in the 40's (that's what below 50 implies). I don't know where the "sweet spot" for heat pumps is, but I don't think it's there.

If, OTOH, you are looking to keep your pool evenly warm and maybe extend your swim season at both the front and back end, that's a different decision tree. I use solar and it allows us to swim, in NJ, usually from early May till late September, rather than than traditional Memorial Day to Labor Day season. For that, a heat pump should EASILY cost far less to run than a gas heater. But if you want to heat and swim in your pool in the 40's and below, then a natural gas heater is probably the cheapest to run, followed by a propane heater.