Again, they aren't perfect, but Shifters have both the Wildhunt and Longtooth, which are more canine in appearance and ability. Far from perfect, but they are there.
There are some furries that really like the lycanthrope idea, but for most ( myself included ) it's kinda worst than no option at all. There are two core ideas to the archetype of Lycanthropes and Shifters. The first is a duality of mind/soul. They're not a singular being, they're an sentient being and an animal forcibly inhabiting the same body. There is always a war between the two, at best a shifter simply finds a balance between the two. Second, they are shapeshifters. As shapeshifters they have no one natural form. On top of that Shifters only exhibit their more animal like features for very short durations. Both of these concepts reinforce how unnatural they are. They're not one harmonious normal being, they're multible things at once. A furry usually wants their furry form to be a normal part of the world.
Serious question: Is not presenting furries and orcs as standard PC races uninclusive?
Saying it would be uninclusive would be an overstatement, but if you want to be as welcoming as possible you need to have those races, and as many others as you can fit in.
Here's some things to think about. I haven't told my parents or brother that I'm a furry. It's not that I think they'd have a problem with it, they're accepting people. It's just that when you tell people it starts a long and sometimes uncomfortable process. First you have to dispel the idea that it's just about people boinking each other in mascot costumes, when that's barely even a thing. Then you have to explain what furries are, and take on the responsibility of being a good advocate for them. You become their lens through which they view the idea, and that can be a heavy burden for some. Then you have to go through the slow process of it becoming normal. Like they might at first try to overcompensate and bring it up all the time in conversations, or buy me things like a hat with cat ears ( please god no ). Eventually it just becomes a normal thing, but it takes time. I'd probably feel better if I went through it, but it's easier to just keep it private.
Now imagine a furry comes to a gaming group and the race they want to play is in a supliment, or worse needs to be home-brewed, and naturally the group asks why they want to play that. Right there in session zero, with people you might not know, you face the choice to have the conversation about being a furry. If a furry race is allowed by default, there is less of a chance that you'd have to justify why you want to play it. Leaving the furry conversation to a later date when you have built a rapport with that group and feel comfortable. It wouldn't be guaranteed, the group might still be playing in a setting where they're not present, but what's in the Player's handbook moves the needle about what's a normal part of the game.
If you create a new default setting for the 6th edition Player's Handbook it wouldn't be difficult to have a large number of races included. Currently the race entries spend a lot of words describing the history of that race and it's place in the world. That's all information that could be shifted to a culture entry instead. This would mean that the default setting would have to have cultures and nations made up of many different races, so no more exclusively elvish kingdoms and so forth. Then you could have about 6 different cultures detailed in the book that any race could belong to, with about 3 pages dedicated to each explaining their history and beliefs, and any mechanical benefits that culture provides. Each race entry could then be fitted maybe 2 to one page, maybe more. That would make it pretty easy to include up to 20 different races.