Harfoots the classic hobbits were the ones we saw in the movies. The fellowship hobbits and the ones of the shire are harfoots. They are described as being shorter than dwarves, having no beards nor wearing shoes.
Stoors are broader and heavier than harfoots and they lived off the rivers.
Fallohides were the thinner, paler hobbits that lived in the woods and dealt with elves.
If Tolkien can have subraces I don't see why we can't. I mean how many variations of elves are there in DnD? Dwarves have almost as many but halflings are like 2 varieties.
Given that my parent edition was 3.5, I only have a passing familiarity with kender so I don't consider them the core halflings of DnD. I'm more of the almond shaped head, sharp eyes, quick wit, trader, wanderer, halflings. I've never had problems giving them the proper feel or allowing them to exist in almost every area of my setting. I would hate to lose all the flavour that is associated with the DnD halflings I know and love for the close minded hobbits of yore.
That being said, I would also love to see them reintroduce true, sit at home, "english", Hobbit-esk halflings but for me it isn't compulsory.