People who oppose H1B oppose it because they think that foreign workers should not be allowed to enter the labor pool thereby depressing the wages.
The bargaining you refer to is between an individual employee and an employer, where the employer obviously has drastically more power, particularly in the case of immigrants on visas. Even having a single-company union would be beneficial, but the problematic companies here would just be non-union shops.
The point of sectoral bargaining is exactly what the H1B system is trying to accomplish, where you establish wage guidelines for the whole sector to prevent companies from undercutting wages with immigration. Except that because the government has to make this one-size-fits-all rule, and doesn't understand the specific needs of each sector, it's hard to come up with the right rule. Under sectoral bargaining, each sector could determine its own needs and goals, and because companies and employees each have representatives, the end result is fairer for all.
(disclaimer, I actually love syndicalism as a concept. In an ideal world, syndicalism could ensure that naive and bought-out politicians wouldn't be able to arbitrarily outlaw encryption - because laws which relate to technology would be in the domain of people who actually work on technology. But like so many systems that sound nice in an ideal world - getting there and making it non-corrupt would be no minor feat).