I didn't say there would be no conflict, but significantly less.
If everyone is an owner, there is no incentive to withhold labor and strike, as they can simply come to a consensus with the other co-owners instead. The only reason unions exist and strike is because of an imbalance of power between the capital owners and the workers that generate the capital, so the unions must leverage their labor as a bargaining chip to try to get a slightly more fair deal. That dynamic is not present in a worker owned co-operative, since everyone is an owner and has the same incentive to increase profit, since it benefits all instead of the few.
This would make everyone pay attention because people don’t really care about anything but long term growth independent of the company’s operating system.
All traditional companies have an incentive to fight the formation of unions, even if they do generate more profits, as CEO's and shareholders do not wish to split up those profits to the workers any more than is absolutely necessary to retain those workers to begin with.
CEO's and Shareholders are virtually all extremely self interested, often times combined with dark triad traits which both encouraged and enabled them to reach those positions to begin with.
They do not act rationally purely in interest of profit, as if that was the case, then they would've already adopted lower working hours, work from home, better benefits, and given partial ownership of the company to the workers voluntarily. Instead, history has shown time and time again that they would much rather let an entire company be destroyed rather than give up power to workers.
You will not have any success whatsoever of convincing existing corporations to embrace unions by proving an example.
A co op would be so different from existing systems that I fear people would think hey that’s neat but we can’t replicate it unless we started over.
There are plenty of examples of worker owned cooperatives, even huge successful ones like Mondragon, which is a multi bullion dollar coop that employs 70,000 workers.
Virtually no existing corporation nor its shareholders would want to become a co-op, because it would mean the inability to exploit and profit from their labor force. Just as they do not wish for unions to impede on their ability to exploit their labor force.