Local Energy Communities (LECs), as a mechanism to incentivize production, self-consumption, storage, and selling of renewable energy, could be particularly interesting in agricultural regions, but the potential for rural LECs remains unexplored. This study models at high spatial and temporal resolution the portfolios of building-integrated solar photovoltaics (PV), agri-PV, wind power, biomass, hydropower, and batteries for forming LECs in all 730 rural Swiss municipalities. By focusing on the self-consumption benefits that often motivate LECs, including consumption for electrified heating, transport and agriculture, we evaluate the national scalability of LECs, as virtual microgrids, under various economic scenarios and incentive schemes. A key finding is that LECs in rural Swiss municipalities could generate up to 8 TWh/year of renewable electricity in 2035, contributing 23 % towards the new Swiss renewable electricity target of 35 TWh/year. However, this potential is contingent on suitable economic conditions (market prices, feed-in tariffs, and retail tariffs) and there is a risk that, under current incentives, LECs might prioritize self-consumption, leveraging only part of their renewable electricity potential and sidelining technologies that could more effectively meet national targets.