I have kids and I am quite the opposite. My interest in them is very occasional. Teaching anything takes a lot of work and they're typically not interested anyway. Most of the experiences they have at school, I have no real insight on. I like to see their interests develop, and I notice that my youngest would probably enjoy partnering with me on some things, but that is it. I'm sure that puts me on some spectrum, but that is how I feel and, whenever a few other dads I know take their guard down, they have a lot of similar feelings - but they cannot state them, because they have become socially unacceptable.
Note also that a lot of what we consider "fatherhood" is a Western construct of the last 150 years, with falling birth rates and diffused wealth. Things were very different when families were poor and sprawling: fathers simply did not have significant time to spend with all their kids, when they had a dozen of them and were out of the house most of the day for work. Significant bonds would be developed only while working together, later in life.