Yes, I absolutely expect these collectives to be less productive than the wealthy class. Does that matter? I’m thinking it doesn’t! The biggest reason is that currently the wealthy take 95+% of the wealth they create, so the fact that they’re more productive has little affect on the workers who live off the paltry wage they are paid. A collective that is less productive but shares more of its profits could pay their workers more than the capitalist companies are. These collectives needn’t compete with non-collectives as the participants of the collectives can opt to buy from a network of collectives whenever possible, providing them economic protection. Finally I think there is work to be done to commoditize robotics hardware and software such that capital costs are low, and this is a key goal of my planned life’s work. The collectives would of course work all in open source, and I think this would lower their costs across the board as there would be no intellectual property to artificially raise costs.
Finally I will say that I agree it sounds unlikely. But think of the outcome! The people would work for themselves and share in the wealth gained by productivity. Instead of wasting away working 60 hours a week until they die, there would be a chance for them to earn more wealth and take time off. It’s a choice of misery or freedom. Even if it’s unlikely, it’s not impossible. And I think it’s a goal worth pursuing.
If the margins in a "wealthy-class-run" company are 20% and they take it all out as profit; then a competing worker collective that's 20% less efficient would have a margin of 0 and no profit whatsoever and no ability to pay their workers more. You can run a labor-heavy shop as a collective (e.g. fast food has had some successes) but anything relating to manufacturing seems just wishful thinking.
Your example of commodity robotics would bring the per-item robot cost down, but that that would make the whole industry much more capital intensive - if robots are expensive, then there's more labor and less robots; if robots are cheap, then you replace more workers with robots and the percentage of capital vs labor shifts to capital. If robots are expensive, then a less automated workshop can compete price-wise with a large, more automated factory. If robots are cheap, then the large factories that get economies of scale on configuring and integrating these robots simply drive down the cost of end product so much that any smaller shop can't compete at all. No matter how cheap robots are, the worker collective can't afford to build as large and as automated factories that the wealthy capitalists can.
A separate point is that if cheap commodity robots would enable worker collectives to run a just as automated operation, then it's impossible for most people who leave their "overlords" to join those collectives - if an industry now has 100000 employees; and because of arrival of very cheap commodity robots the results can get done with 10000 employees, then it doesn't matter much if that revenue gets taken by a capitalist employing 10000 laborers; a worker collective of 10000 people; or 5000 / 5000 in tight competition... then it doesn't matter because 90000 people have to leave the industry anyway, even the worker collectives have no need for them.
Let's use self-driving taxis as an example of automation. Let's assume that some time in the future, cheap commodity "robots" driving cars enable automation for most of taxi driving. In the "capitalist overlord" scenario, Uber runs and manages self-driving taxis. In the "workers collective" scenario, a bunch of current taxi drivers form a collective, buy "commodity robots" i.e. hardware that makes their cars self-driving (to have comparable efficiency/price with competitors) and run and manage a company that competes with Uber... but they won't drive taxis anyway, they're maintaining and managing a self-driving-taxi company that doesn't need much if any actual drivers. Now what's the practical difference between them forming a "workers collective" versus them buying shares in any other self-driving taxi company? In both cases they're the owners, but not the workers, because their work has been made obsolete by automation. In both cases they get their income as rent on their capital, not wages for their labor; at least not most of them. If they can't afford to buy the shares, then they can't afford the capital investment to start an equivalent competing company, those should be pretty much the same amounts.
Regarding efficiency: that’s a good point about lower efficiency leading to zero/negative profits, and this reflects a reality for many workers collectives today. That said, I would expect these collectives to charge higher prices, perhaps 1.5-2x as much, and let consumers decide. I’d definitely rather pay more for quality goods that support a more fair system, and usually find it difficult to do so.
Regarding collectives versus buying shares: a key and significant difference with collectives is the notion that each member has equal voting power for decisions made within the company. Shareholders meanwhile have less control, owing to the power of the board of directors. Concentrating power makes anti-social behavior more likely, as the class difference between the board and everyone else means decisions they make may not affect them the same way they affect others. This is significantly less pronounced in a coop as I describe, so there is less anti-social interference caused by businesses in this scenario.
You have other good points I’d like to reply to, but I’ve got to run. I just wanted to mention that a key thing I feel you are missing is that working for and a society made up of worker cooperatives would lead to a qualitatively different life. It’s not a pure apples to apples competition scenario as I am advocating that people actively make buying and employment decisions based on a desire to realize this new cooperative society. I agree with you that absent ideology, the capitalist organization would crush the coops based solely on a selfish purchasing decision. That is, the capitalist products may be cheaper and may be better (or not), but I still believe a coop can survive and thrive if enough people choose to stop supporting the capitalist way.
These terms are a bit loose by the way - I stil describe a scenario rooted in a fabric of capitalism. The coops sell to each other based on markets if they want, or other agreements if they want. No government interference is required. And I advocate that these groups behave in intentionally pro social ways. It takes devotion and energy and heart. It is not for those simply looking to make a buck.
In late 19th century capitalists absolutely relied on laborers to create their wealth, in late 21th century capitalists rely on investments in automation to create their wealth, and they have limited need for the lower class laborers. Already right now there are millions of jobs that could be automated but aren't just because you can get dirt cheap labor to do it manually (e.g. textile/footwear industry in SE Asia) - and as soon as the laborers start asking for decent income (or simply the tech falls in price, as it does over time) the laborers will get replaced with automation.
And the displaced workers won't be able to form productive collectives, because in that economic scenario, to be productive and efficient, you need to do the same thing with few people and lots of (expensive) machines; the whole reason why they become displaced is that most of their labor objectively isn't useful anymore - it won't become any more useful if they form up into a collective.