The word "daddy" has been so sexualized to the point to where if I have kids (highly unlikely scenario, since I use Arch Linux), I'll just have them call me "father".
it's certainly not the norm to call parents by thier first names in a loving way, but there's no reason it has to stay that way. Most people don't use nicknames for their best friends, siblings, some people even use first names with their spouses, and that doesn't mean these people are loved any less. using first names isn't inherently distant/cold.
but at the end of the day honestly I think what you call your loved ones isn't that important so if you're more comfortable using mom/dad, that's ok too
my siblings do this. it mainly worked/adapted to this because:
our parents gall each other with the first name
it was annoiying for them to differentiate our 5 different voices to all the other childs at the playground or parades and other public events where a bunch of kids where present
Edit: and i like the system more because i was very annoyed that i had to call other parents: {friends} mom, can i have a drink? because never heard their name. Thatvwas already infurating during kindergarden times
that's a really interesting perspective, I guess it might also be difficult for people who have friends that share a first name with their parents, I could totally see not wanting to call your dad John if that's what you already call your best friend.