Transition pathways for Europe to achieve carbon neutrality emphasize the need for a massive deployment of solar and wind energy. Global cost optimization would lead to installing most of the renewable capacity in a few resource-rich countries, but policy decisions could prioritize other factors. We investigate the effect of energy independence on Europe's energy system design. We show that self-sufficiency constraints lead to a more equitable distribution of costs and installed capacities across Europe. However, countries that typically depend on energy imports face cost increases of up to 150% to ensure that they cover their demand on an annual basis. Self-sufficiency particularly favors solar photovoltaic energy, and with declining PV module prices, alternative configurations like inverter dimensioning and horizontal tracking are beneficial enough to be part of the optimal solution for many countries. Moreover, we find that very high solar and wind annual installation rates are required, but they seem feasible considering recent historical trends.