That works if this is a "one time game" (game theory) as opposed to a repeated game.

If an employer does do training, it means they'll probably continue to do more training over time, which helps the employee become more valuable.

If the employer doesn't do training, yes they may be able to allocate the training budget to salary, but they are not going to spend anything training you or letting you work on projects to increase your skills while you're there, unless they absolutely must.

I think people also have some human perception of how they're being treated, and prefer to work for people that invest in them.