What you are describing is what existed before what we have now. A group of people working for an employer would try to negotiate for safer working conditions, better benefits, etc. The employer would take the list of demands, fire the person who handed him the list and say, "I'm not giving you any of this shit and anyone who talks about it again gets fired too."

So people started organizing by trade. It made sense because workers of a common trade share experiences and grievances. If one particular employer treated its workers bad, that trade guild had more leverage by threatening work stoppage against other employers who could put pressure on the first employer.

Over time employers started to converge and grow in power. Now you have a company who employs thousands of people in multiple locations. To keep the balance in power, the unions converged and grew in power. You cant threaten to replace a union worker if everyone who does that job is in the union(1).

Now the unions are big enough to disrupt economies, sway elections, etc. They are large professional entities of lawyers, financial managers. They want everyone in the union for maximal leverage (ie fewer scabs, more dues) so they lobbied to affect the policies we have today.

The small voluntary no-admin-overhead organization you are describing is ideal, but its really unlikely to work. It would depend on the employer allowing it to happen.

I could say more here about the growing wealth gap, criminalization of poverty, and the quiet ongoing class war, and end with a Malcom X quote, "Anytime you depend on your enemy for a job you're in bad shape." But I dont feel like saying all that. ;)

1. robots