There are a couple of points that I can think of.

The Spitfire indeed has a high number of survivors, anywhere between 40-50. These were also still in production after WWII, with the last aircraft retiring from active duty in 1961 with the Irish Airforce. In addition they were widely used amongst various allies following WWII, and used the Merlin V12 engine found on various allied aircraft which was license built in the US as well.

BF-109, there are around 30 survivors, but these include a high number of HA-1109 / HA-1112 conversions (Spanish license built Bf-109's) These were used in making the Battle of Britain movie. Spain didn't retire it's license built Bf-109's until the late 60's. Also, Czechoslovakia continued to build them in license until 1949, completing an additional 550 airframes under the Avia S-99 / S-199 designation, using the original jigs and tooling.

The Il-2 was only produced between 1941 and 1945, and it's use following WWII was not really extensive as it was considered obsolete. the last active Il-2's were decommissioned in 1954. This in contrast to the Bf-109 and the Spitfire whom were further developed and used long after WWII, and thus retained a wide support base and the tooling required to produce and maintain them.

Additionally the Il-2 suffered major losses during the war on the eastern front due to its inability to perform in air to air combat when faced with enemy fighter aircraft. Numbers produced according to Wikipedia (it's a Polish source, I don't have it in my personal library unfortunately) are roughly 38,000 units of all variants lumped together.(1) Total losses of air to air combat alone are over 10,000 units (2). Unfortunately I couldn't find figures for the losses due to aa fire.

Also, I think it would be unfair to compare them to the Spitfire and the Bf-109, these are fighter aircraft whereas the Il-2 is a ground attack aircraft.

Another reason might be a difference in memory culture between Russia and the West. Unfortunately this is speculation on my behalf but perhaps there is someone who can pursue that line of investigation. Bf-109's and Spitfire's were extensively used in the making of movies like The Battle of Britain and numerous others. Also the prosperity following WWII in the west meant that probably a larger number of aircraft fell in to private hands, and as already stated, engines and parts were readily available. A good example of this is the Confederation / Commemorative Airforce (CAF) established in the US in 1957. (3) Unfortunately I do not know enough of the situation in Russia to say this is an definitive awnser to your question. I do hope my answer gives you some insight.

(1) Alternative source: https://airandspace.si.edu/stories/editorial/stalin’s-ilyushin-il-2-shturmovik (2) Bergström, Christer. Bagration to Berlin: The final Air Battle in the East 1944–45. p.132 (3) https://commemorativeairforce.org/root/airplanes/ghost-squadron/91-caf-aircraft/211-caf-foreign

Follow up question:

A dozen Bf 109 airworthy? Or do you mean the HA-1112 Buchon?

Besides the points already mentioned here, two things worth remembering are, first, most aircraft contain valuable parts and metals that can have considerable value as scrap. Given the very real shortages of raw materials in the immediate post-war years in Europe, it isn't much a wonder that most old weapons that could be recycled, were recycled very quickly.

Second, storage space costs something, too. What happened to many old airplanes was that they were either broken up for scrap outright, or left in an unused corner of an airfield somewhere, exposed to the elements. The more valuable parts were usually removed right away, and what was left was often just the fuselage. After a decade or two, there was little enough left in a worthwhile shape; and we need to remember that wartime planes were often built with an incredibly short lifecycle in mind, which meant that they often weren't that durable to begin with.

Finally, there wasn't much appreciation for old technology until fairly late in the 1970s. (This was somewhat of a chicken-and-egg problem, since as long as there wasn't suitable storage spaces or museums, there also weren't many alternatives.) In Finland for example, countless old airplane hulks, including the last surviving examples in several cases, were burned in midsummer's fest celebrations at airfields, or to train firefighters. That was simply the custom back those days, and no one seemed to mind much.

Generally it's private enthusiasts that keep those things flying. Due to Soviets negative relationship with private property, buying one from them would have been hardly possible. I guess there was a possibility to launch a campaign under the guise of something like Komsomol, but just this factor made it hard.

Another reason is that keeping old planes flying is really expensive. You not only need storage and fuel, but also pretty much a whole workshop capable of producing spare parts for them or some other way of procuring those. That only flyable IL2 you mentioned actually has lots of non-original parts including the engine. There's a team in Samara that is currently working on rebuilding one using completely authentic parts.