Serious question: I've never quite understood the "what if you have a kid" argument. Is it the company's fault you had a kid? Why are they obligated to pay you more because you had a kid? If you were worth $100K and you negotiated for that, then that's what you make -- a kid has nothing to do with it.
Put another way, let's say we both make 100K in salary, and then, all other things being equal, you have a kid. Do you get a raise to 120K just because you had a kid? I didn't have a kid. Don't I get a raise too?
I think you're looking at this wrong. The kid is an example for why the budget gets tight, it could be anything (buying a house, deciding to pay off your credit card), you're correct the company has no obligation. Hence why you're asking, not informing that they'll pay you $20k more.
"If you were worth $100K and you negotiated for that, then that's what you make" was true at the time of the initial negotiation. This is a separate negotiation, with a source "hey, company X will pay me 20% more"
No, you don't deserve $20k more as you didn't ask for it, you might if you reopened negotiations.
No, you don't get a raise, because you didn't ask for it. The difference you should be focusing on, in your scenario, is not that I had a kid. It's that, for whatever reason, I renegotiated my salary. If you can do the same, then you get the same results.
See, whereas you never quite understood the "what if you have a kid" argument, I never quite understood the "don't I deserve the same as that other guy" argument. The way I see it, the magical answer is always the same: maybe you do. Do something about it and you might be surprised.
Put another way, let's say we both make 100K in salary, and then, all other things being equal, you have a kid. Do you get a raise to 120K just because you had a kid? I didn't have a kid. Don't I get a raise too?