Yes, and emotions help you choose good “anything”s. There’s always an emotional superstructure- yours, or somebody else can choose for you, based on their own motivations.
Ok that is a valid truth, however the growth mindset embedded in the sentence "I can become good at anything." is not that.
Its that maybe you can't become the fastest man on earth. That guy exists, his name is Usain Bolt. However, you can for sure get good at sprinting, even if you are missing parts of your legs. That guy is Oscar Pistorious. Maybe you have COPD and you can't? Well, you might need to adjust "good" to be a winnable opportunity in your capabilities. Maybe this is walking to the mailbox. If you couldn't walk to the mailbox last week, I'd call that "good".
Here is the opportunity for the emotional part you mentioned to arise, so yeah, I agree.
Emotions, sure. You can become good at managing your emotions. You can become good at navigating and integrating the superstructure of society into positive outcomes in your own life. You can become good at public speaking and swimming and programming.
You likely will not be able to become the best in the world at anything at all, but you can become good at anything.
