My resolved in its default configuration will try appending .local and search via mDNS if no results are found via the DHCP provided server. I believe macOS does the same.
Ping foo on my machine results in foo.local being successfully pinged. Your mileage may vary.
> would potentially use mDNS if you have a ping that does such a thing
It's not a feature of ping, it's a feature of the name resolution setup on your machine (nsswitch and/or resolved on Linux).
> Rather, most routers add DHCP hostname requests to the local DNS routes
What do you mean?
Rather, most routers add DHCP hostname requests to the local DNS routes. That doesn't require mDNS, nor would you want to replace it with mDNS as mDNS is more limited & flakier.