No, there's not much of a legal avenue to force professional sports leagues and unions to let other companies make games that utilize the likenesses of the players or names and logos of the teams. Certainly not using the examples in OP's post. Exclusive licenses like this do not represent a monopoly, nor do they represent unfair business practices. And you, as a fan, do not have standing to argue brand damage.
And as far as spite goes, the simple fact is, even if FIFA chose to offer a license to another developer, you're simply not going to get an EA FIFA competitor on Switch that remotely matches the quality of PS4 and XBox. The Switch's limitations were always going to result in things like this, and it will get worse as the 9th generation begins in earnest.