To first answer the question. For many, almost all older aircraft you may avoid leaded fuel in one of two different ways:
- Fly on mogas. As mogas is simply a mix of various stuff you take your chances that one day the mogas will be "off" enough to create a problem. (First check that all rubber components and inside tank coatings and stuff like that can handle alcohol).
- Fly on one of the unleaded Avgas formulations allowed by you engine manufacturer. Type and availability varies between locations. As aviation engines has a limited life span, often on the order of 2000 hours, you could probably convert you plane at next engine change without any extreme extra costs.
Now a few words why it has not happened. There are two different problems around the move to unleaded aircraft fuel.
The first problem is related to the supply side with 100LL beeing a niche product, used in diminishing volume over time. There really is very little economic reason for the fuel providers to introduce and sell and support one more type of aircraft fuel at airfields. It is possible to find unleaded aircraft fuel in some markets and they tend to work very well without any specific problems for the airplanes that can use them.
It might be tempting to assume that you could switch to mogas straight away. And it will often work, but without guarantees. Gasoline is a mix of various stuff, where the producing plants selects the lowest price components at any time. As such there is no guarantess that mogas will have the same composition from time to time, except that it will work in most auto engines. The production might involve changing the composition so that it is "thicker" in summer (as the thicker components might be cheaper) which generally is no problem for autos. But aeroplanes fly high up where it is cold even in summer, and the thicker components may freeze. Avgas 100LL (and other aviation fuels) have specific limits on what temperature they should be able to sustain as well as how high up at lower air pressure they should not boil off. The limits for mogas are often not really defined. In addition mogas often contains alcohols, metanol or ethanol, which is no problem for a modern car but can dissolve certain rubber or plastic components used in older aeroplanes -- remember they were never expected to handle alcohols. Regardless, lots of smaller enginges and smaller operators run on mogas without experiencing problems.
The second problem is the structure of consuming side of Avgas. The main part is used by the larger two motor planes used by aviation companies for short hops or special flights. These tend to run under commercial FAA rules, meaning that they have to follow all regulations to the letter. And one of the regulations state that the fuel used should follow the engine manufacturers minimum requirements. And they seldom allow the use of anything else than 100LL for their larger turbocharged engines used in these planes that use most of the 100LL. As the engine manufacturers will be responsible, possible sued for damages, they have a difficult time allowing mogas. They could start programs to certify unleaded aviation fuel but it may need degrading performance on the large turbocharged engines -- after all the 100LL was "invented" to allow high performance. For smaller aircraft engines this has often already been done and they allow unleaded fuel. But as the larger engines have not been certified, even if the fuel company would offer unleaded fuel at airports, the largest buyers would not be allowed to use it, which sort of completes the cycle.
I believe that the change has happened already or is very imminent when it comes to smaller, private type of flying -- they can and often do fly on unleaded fuel. For the larger planes flying commercially and beeing the large buyers of 100LL my guess is that they will over time probably convert to Jet fuel instead, most probably by completing the change over to turboprops or perhaps diesel type engines.