I just booked JFK-BOG with delta, was inquiring with the diamond desk about prices for infant (lap) if the adult ticket is bought with miles or paid, I was pleasantly surprised (or not) that if the adult was a paid ticket infant ticket would be a total of $134 but if adult is booked on miles it was 0 miles and $74.97.
Another experience I’ve had (though might not be too relevant for many here) is that when I came back from my last Eretz Yisroel trip with delta TLV-JFK I used a global upgrade certificate for myself and a few weeks later (a few days before the flight) I get a call from delta asking me to pay a few hundred $$$ on top of what we already paid since now it was a business class ticket and baby needs to pay 10% of the fare plus business class taxes!! Any argument that I used an upgrade certificate and didn’t actually spend a cent on this didn’t help. So I just moved my baby to my wife’s ticket who was in economy (we did it like this so baby can be in his car seat and we switched off mid-flight)