No. Not if you understand how unions work.
Professional sports leagues have unions because they are necessary. There is exactly 1 league, and you’re required to sign exclusivity contracts with your team. You are owned by your team. You play for them, or you don’t play at all. You move your family to whatever shitty city bought your rights. Only rarely does a player get any say, unless they’re a superstar with a special contract. They’re also very prone to injuries that can take them out during their narrow prime earning window, and that risk needs to be hedged. As does the risk of permanent damage, including brain damage, by being required to play when it is not safe. And NBA players actually got paid very poorly before the union. Far worse than software engineers. They had no leverage.
There are many reasons for players to have unions, and none of them apply to software developers.
The Hollywood situation was similar. New actors were locked up in bad contracts. But generally, all of Hollywood is a mess of negotiations, unconventional and confusing compensation structures, scheming lawyers, and conflicts of interest all over the place. These also don’t really apply to software developers.
We don’t have agents, royalties, multi-year exclusivity, or a huge population willing to fight for scraps and slave for free in hopes of getting a big break (game development - which has much more in common with Hollywood - being an exception).
Unions are not free. The layer of bureaucracy that they introduce is a huge cost, and one that many companies cannot bear. Startups definitely can’t. Then you have to account for the widespread abuse by employees in unions. Your salary has to subsidize everybody who decides they’re going to be lazy and take a free ride by exploiting union rules. Those people are everywhere in unions. And it’s completely rational. Most people will do the minimum required for the maximum take, especially when there is no risk to doing so.
Sometimes, this cost is worth it. But, if we ranked industries in need of a union, I can’t really think of anything that would have less need for a union than software development.