The only phones that have ever come with root out of the box have been dodgy backstreet Chinese ones, and that was probably because they didn't care.
Manufacturers don't generally approve an actual rooting method, because rooting means altering the system software, which also interferes with future over the air updates (and nobody wants to maintain 2 sets of OTAs for rooted and unrooted, never mind the fact that once people root they generally change other things). And of course the manufacturer isn't going to want to be responsible for everything that the user might get up to with root!
But there are a number who provide official ways of unlocking the bootloader, after which you can just flash a custom recovery (if one has been made for that phone) and use it to root. Pixels are an obvious example, Essential were very open, OnePlus are unlockable. Sony always used to be (but it would have an impact on some of the media software, so caution needed), not checked recently. HTC have an official unlock, and since nobody's had an update from them for ages you don't need to worry about it interfering (sorry, couldn't resist!). Don't know much about Moto or LG. You won't get official support from Samsung (and US Samsung's are amongst the most hostile to root), and slightly surprisingly Nokia do not have an official bootloader unlock either.
