The sad thing is, there have been people in the past who've attempted to provide such a place, but somehow didn't have the necessary public interest. Martin Newcomb was one of them; his Museum of Synthesizer Technology in London, which had over 350 instruments, was shut not long after it opened. I came across this article the other day which includes an interview with him.
Admittedly, Martin didn't initially have a museum in mind, he simply needed a place to store his growing collection. In fact, he was enthusiastic about electronic music early on but everything was extortionately priced at the time so he couldn't afford a synth until later in his life. He says - "I think a lot of people have a passion for certain things, but usually it stays latent unless they can afford to do something about it." (He could not have been more right there.)
"I gave the museum my best shot, but not enough people gave a damn. Most people were more interested in seeing how long it would be before it collapsed”. I couldn't quite process that. At this point I'd love to say that this is an April Fool's joke, and that Martin's Museum is still up and running, and that hundreds of people have visited it since its opening, etc, etc, but I'm afraid that would not be the truth.
On the up side, the knowledge that people in the past have made wholehearted attempts at making synths more accessible for the public is an optimistic thought. And who knows, maybe it's all still to come...