Ownership is one part of the model, and I think you have a point that it's more diffused in many startups. However, I'm not sure democratic control of the business is part of the startup model. Correct me if I'm wrong, but I think they tend to create a traditional management structure with CEOs, etc.
Co-Op is a very loose term and comes in many flavors.
It would be a bit naive to think that they are inherently better managed or more "democratic" (egalitarian?) than a regularly run business. Like any democracy, not only do they come in different flavors (ie, representative democracy vs "pure" democracy etc), but they come with their own quirks of implementation. In many democracies the individual voters have little actual power and organized and concetrated special interest groups game the system. And there are plenty of co-ops run by CEOs.
And most co-ops do not offer order-of-magnitude improvements in working conditions or pay. You are looking at a 10% type improvement, not a 10x one. The downside of a co-op is that it might have a 10% improvemnet in (potential) conditions, but a poor implenetation but will be -10% as productive due to inefficiencies and execution problems.Which basically runs the risk of zero net improvement for the typical person there.
All of which means that you really need to analyze any proposed or actual implementation. Broad-brush generalizations are often misleading in this context. Just something to keep in mind.