Oil and gas wells use to be far from electricity consumers, and transporting hydrocarbons by boat needs less investment than electricity by a power line. In addition, wells give C3+C4 at the same time that they produce methane or oil: irregularly, when the main customers needs it, not when the electricity consumers want. So for the electricity mass-market, I'd say it's better to transport the hydrocarbon to a power plant near the consumers.
Make electricity for the needs of the well: maybe. It's just that the teams need electricity when the well doesn't produce or before it does, and in amounts negligible with the well's production. So they have Diesel generators from the beginning; you may try to convince them to purchase a propane turbine too.
Liquefy and store briefly the C3+C4 at the well, have special boats (easier than methane, true) to carry it to main power plants or refineries? That sounds better.
Gas turbines run more easily with propane+butane than with methane or coal and lend naturally to a combined cycle. At a big power plant, your competitor is coal and presently shale oil+gas, which are cheap. Though, shale oil already depletes, and propane emits less CO2 than coal, so you might feed some power plants with them.
My gut feeling is that refineries would make the best use. Hydrogen is useful and propylene must presently be converted from ethylene to make enough polymer; butylene (mainly iso-) is a big feed of alky units.
What proportion of C3+C4 is flared at the well? No recent information. Few decades ago, it was: all, except at few wells. Maybe two years ago, oil and gas producers committed themselves to flare a bit less of them.