I don't really have an opinion about this one way or another, but would like to point out the following:
As a professor with external funding, I run a small business. I bring in money from a customer (for example the Federal government) and spend it on salary for myself, postdocs, and graduate students. I get in trouble if I have contracts for which I have no employees ready to do the work. And I get in trouble if I have employees but don't bring in enough money.
If this was a regular business, it would be my choice to set and negotiate salaries. I would also have flexibility in hiring and laying off employees. I would budget as much money as I think it takes to complete the work.
But this is not how it works in academia: graduate student salaries, for example, are set by the university and not me as the employer. And at least in some disciplines, graduate students are hired by the department and only leave when they graduate. As the one who pays their salaries, I have little flexibility to set the terms.
This is occasionally an awkward position to be in. Unions would complicate this because it means that issues such as labor relations, salaries, etc. become even less predictable to me. I already have no real input into their salaries and terms, but at least I know that they are predictable because they are set by the university or department, and I can anticipate what they will be 2 years from now. I might not be able to do that any more to the same degree if there were unions. That matters because I may have a contract that runs 3 or 5 years, with a fixed amount of money and work to be done.
All of this is independent of the moral question of whether employees should be represented by a union. Having grown up in Europe, my take on that is that unions are good.