Standalone recharge anywhere... As said, the wing surface is too small, the aircraft will likely get grounded several days... Why not just put an array of solar panels finely calibrated for efficiency at many airfields ? Charge would complete fast, and work for a broad variety of aircraft size, ground vehicles and equipments ? The ground array would be easier to maintain and upgrade.
Wings aren't rigid ! Common misconception is "it has internal structure, therefore, it will remain straight..." Actually, over a couple meters, a wing bends. At microscopic level, it slowly deteriorates over time (wrincles/cracks). A layer of solar panels will rub the wing surface at contact level, especially along the edges and at the corners (is it glued or what ?). That's a technical issue, how often it has to get fixed to keep that upperwing clean (ie no aerodynamical disturbance) ?
Weather ! I know solar panels can be reinforced to withstand hail. In aviation, this translates to weight and extra costs. That's usually a big NO.
Efficiency. Solar panels lose efficiency with dust and scratches (we ignore the other causes to focus on those). Snow, dust, rain, hail... Even if it's just for supplement purposes, it has to be maintained well to have a meaning : how much hassle to care for ? What to do before each flight, what to do between flights ? What could go wrong if not properly handled ? Practically, the amount of care is much concerning than adding another battery, as mentionned.
Maintainance : One way to gain or lose money in the aviation industry is how much of a cost is maintaining engines and systems. Who's (company/subcontractors) in charge of ensuring maintainance of those solar panels ? If it's a small company only present in a few states in the US... You either need a company that can handle problems whatever the country, or a company that can qualify personnel, or a company that uses OEM components any developped country can produce (and not charge too much for patents...) - likely a combination of those.
Please rest assured I'm not here to discourage all efforts in building environmental friendly systems, components and behavior, but for practically everything, the purpose must have a meaning. An aircraft is meant to move people or goods over terrain or faster than any other way. To be efficient, weight has to get "donated" to payload as much as possible instead of structure, equipment and systems (unless safety is a concern), and the vehicle has to be as less of a hassle as possible to operate (unless safety is a concern). Your question ask for the "why not" rather than the "how to", therefore, we focus on the purpose, not the technical issues that can be solved in a way or another.
Experimental aircraft are nice, but sometimes, they fail to remember what was the purpose... You can build a self sustained fully electric aircraft, but if you can't put people and cargo inside, and/or it requires special care (qualified people, frequent checks, logistics/equipements, spare parts manufacturing...) on a daily basis which translate to utterly expensive costs the end user (you and me) has to pay...
On a related yet distant topic, it's very similar to "flying cars" : the purpose is to safely transport people over cities... quite a major safety concern : how would you ensure the everyday lambda anyone is qualified enough to actually fly that thing ? That's the answer why over 2 centuries of dream, yet, the drones-like advertised vehicles are still a long way before taking off from our backyard. The purpose, it being safety and/or "economically viable", should be at the center of the design process, from the start, not a concern one solve later. For an aircraft, you freeze payload and range first (for example), then you solve every major safety issue (means a LOT of dead weight), then you solve all other problems and assert if adding solar panels is a bonus or a malus. Not the other way around.