It was never really an open system. The firmware was closed source (you could eventually buy an unofficial disassembly) but you couldn't update it with your own changes. You could add external hardware, with some effort, but it was never trying to compete with a backplane system like S-100.
What it did have - apart from very low initial cost and wide availability - was instant-on (no formatting, no setting up, no downloading and installing), staged progress from beginner to expert (i.e. from BASIC to assembler), a small comprehensible system (the manual explained everything BASIC could do, assembler needed an extra book or two but was still very manageable) a very large market with very low cost of entry and high margins (you could write a game, advertise it for almost no money, and send out the initial copies from home with no duplication costs), and a supportive culture of print magazines, occasional TV news and documentaries, and computer shows. (Face to face clubs were much rarer and less influential.)
The physical case design was just plain cool. And it worked with your own TV, which was almost like being on TV.
So basically a combination of instant gratification, tiny-system simplicity with tough constraints that rewarded clever solutions and creativity, low-friction financial opportunity, cultural reinforcement and support among peers working at a similar level, distinctive aesthetics with a coolness of a sort, and affordability.
I don't think it's a coincidence that it happened not long after punk and synth pop in music. Even if their output was very different, all of of those had very similar cultural features.