I'm sorry to say this but you are uninformed. Dogs have immense utility! These days yes they are generally house pets but they greatly improve mental health and love you unconditionally.
Dogs are also used as ratters, herders, and as protection for livestock from predators like foxes or lions (depending on where you live...). So much so, some working dogs can go for 50k in Australia!
Dogs require upkeep in the form of food, water, vaccinations, training and toileting.
As such the description "free as in puppies" is apt.
For the purposes of communicating with larger audiences, I'm assuming the general experience with dogs, which is typically as a house pet. You're correct that a free working dog is a different scenario, but qualifying the idiom loses something. I don't see "free as in puppies suitable for work you can make practical use of" catching on.
Dogs are also used as ratters, herders, and as protection for livestock from predators like foxes or lions (depending on where you live...). So much so, some working dogs can go for 50k in Australia!
Dogs require upkeep in the form of food, water, vaccinations, training and toileting.
As such the description "free as in puppies" is apt.
Have a good day :)