How long of a long term are we talking about? I suspect this is very dependent on many factors (not least of which is labor, but also insulation, climate, etc).

The energy (gas+electric) bill for my whole home would've taken well over a decade to add up the amount the mini split installation alone would've cost, so even if it brought down my energy cost to zero (which it wouldn't), it would've taken a decade to pay for itself (including the cost of window units).

Edit: and yes, they're prettier than window units for sure, but as you've pointed out, they're not competing with window units. They're competing with ducted central air that has almost no visible impact.