Why is alcoholic gasoline such a showstopper for aviation?
The modifications required are just not economically viable.

The main issue is vapor lock, because ethanol has a lower vapor pressure (i.e. more likely to vaporize) than gasoline.  Worse, mogas ethanol levels are varied to achieve ideal vapor pressure for different temperatures.  This is fine for cars that go through a tank of gas every week or two, over a relatively small temperature range, but a serious problem for planes where the gas may sit for months and then experience a wide temperature range at different altitudes in a single flight.

Vapor pressure matters because engine-driven fuel pumps, which are the norm on planes, pull fuel through the fuel lines.  Especially when combined with low wing tanks, ethanol may vaporize in the lines and block any further fuel flow, which is a far more serious problem for a plane than for a car.  Pure gasoline has a high enough vapor pressure that doesn't happen.  When ethanol was first added to mogas, carmakers solved this by moving the fuel pumps to the tank so the fuel is instead pushed through the fuel lines and therefore won't vaporize regardless of its vapor pressure, and given normal fleet turnover, that was the norm within a few years.  Some planes do have tank boost pumps like cars, but they are usually not intended to be run full-time; ethanol would require tank boost pumps that can run full time, which means either replacing the existing ones or adding new ones.

Ethanol is also more corrosive than gasoline.  Using ethanol regularly may mean replacing fuel pumps (both engine and, if applicable, tank), fuel lines, seals, injectors or carbs, etc.  To make such modifications, you'll need an STC for each.  Developing an STC is expensive and the market is quite limited, so the companies selling them need to charge a lot to recover their costs--on top of the high cost of the parts themselves, which have the same issues.  Also, while many engines were retroactively rated for mogas (even with ethanol in some cases), you still need an expensive STC to change the old placards that require avgas.

Also, while not directly related to ethanol, mogas doesn't contain lead.  Older airplane engines still require a tank of leaded avgas occasionally to lubricate valve seats and guides.  That can usually be fixed by replacing certain parts with newer ones made from newer materials, but that's not cheap either and usually best delayed until the next overhaul.  Until then, you can't run mogas full-time, regardless of the ethanol content.

Once you add up all these costs, retrofitting most GA aircraft for ethanol could easily end up being more than the planes are worth.