If I'm talking to you, I ask you. what if you upset your boss tomorrow and he/she let you go? What do you do? How easy is it to find a job, or more importantly, a good job that benefits you? These skills are useful there.
Side benefit, these skills can make this job easier as well, though it might be hard to get people to change.
For the boss,
we're going to be in this business for awhile. We could get more done, and get new people up to speed, and we can respond quicker so less people complain to you (or give you more money). Let's slowly try to make things better. Again, self-interest.
FWIW, I would not learn K8s beyond just understanding what is does. It's too big a management hassle and the benefits require a lot of changes from a lot of things. Going to containers is not easy, simple, or quick. It's not pick 1 or 2 of three, it's all three are hard.