I pay $45/month for the 100k whole life policy. My rationale is that I like to "stache" money away in a variety of places, why can't this just be one more at a small sum of $45/month. If I get hit by a bus tomorrow or in the foreseeable future of my son's youth, it will be worth it. If I live for many many years my investments will surely outweigh the payout and interest this gains, but it might be a nice "icing on the cake" for my son and/or grand kids.
Rather than critique whole life itself (easy enough to do), let's cut directly to why your rationale is wrong (sorry).
Your rationale, above, boils down to: if I die, my son gets 100k, if I don't, it's an extra 100k anyway on death (as "icing" on top of other investments) and it grows as an investment.
Here's why it's wrong: you aren't comparing the alternative, which is term life + investing the difference.
If you instead had term life for 100k, you'd still have the death benefit of 100k (whether you die soon or later), and investing the extra money that you save from term being so much cheaper means you'll end up with more money (aka even more "icing").
Whole life, with its higher fees, is just going to leave you and/or your son or other beneficiaries with less money. That extra money goes to the insurance company, instead of them.
Life insurance may make sense for you. But term gets the same death benefits, while giving you more money to invest at lower fees, ending up with much more money in the end.
Thus the error in your reasoning. If there wasn't such a thing as term insurance, maybe it would be worth it to have whole life and the more expensive fees in order to get that death benefit. Since term insurance IS available, whole life is not worth it.