So far it’s worked. But I haven’t had the decades of experience yet to reflect on it.
As I see it, that's my manager's job. He's always blathering on about aligning with this or with that, but I have more than enough work to keep me busy and if he wants me to work on something else, he will tell me. This has worked well for me for 2 decades and I'm more than satisfied with my benefits and compensation that I'm happy to just keep plugging along.
No, it's your job, because it's your future at stake.
Never put your destiny in the hands of others.
Your manager needs you to bridge the gap between when the company was doing yesterday (this is what is making the money today), and what the company will do tomorrow. When your manager sees that next year they will need a skill and gets you to develop that skill they have your domain knowledge of the existing product to apply to the next thing and the whole gets done faster because of your experience and new skills.
You are responsible for yourself. If the next job is a variation on what you did today no training is required so he won't give it - it makes you less valuable to outsiders so you won't leave. Also because you are not growing he doesn't have to give you top raises to keep you from leaving - which is more money to give someone else who is better than you. The downside of this is you need to guess where the next big thing will be and sometimes you will be wrong.
If your goals are too closely aligned with the company's, you risk devaluing yourself for your own or the next company's goals. If your goals are too different from your company's, you risk finding yourself out of a job.