As a player, I'm wary of DMs who run fairly standard D&D campaigns but restrict certain races, often for seemingly arbitrary reasons.
No dragonborn in my game! Why? Because . . . I don't like'em!
Now, if a DM is using a specific campaign setting, published or home-brew, or is going for a particular genre feel to the game . . . I can dig reasonable restrictions on character options. It's just that most of the DMs I've run into who are adamant about restrictions . . . run very bland settings. World-building by restriction alone is not my cuppa tea.
Ideally, I'm cool with a DM providing a
whitelist (a list of appropriate options) for their campaign idea . . . but being open and willing to go off that list if a player asks and has a cool character concept. DMs with strict
blacklists (banned options) and no room for divergence . . . eh, I'll find another table, thanks.
Of course, with the variety of character options available today, if you play with no restrictions you can easily end up with a party looking like
@Hussar's group!

(
I kid, your game sounds fun). If an eclectic party of different anthropomorphic animals (
a tabaxi, harrengon, tortles, kenku, loxodon, and a dragonborn) wanders into a typical D&D town populated by humans and demihumans, it can be off-genre for the DM. Of course, nothing really wrong with crazy party make-ups, if that's what everyone at the table is into!
What I'd like to try, but haven't yet . . . is a lottery system. Something that would have all options on the table, but result in a more traditional party make-up. Think of the "party" for the OT Star Wars films . . . mostly human, with one exotic alien and two quirky droid NPCs. For classes, players would draw cards randomly for a hat. Each card would have a category, perhaps
arcane,
divine,
warrior, or
rogue. Players could choose any class that fits within the category drawn. Next, draw cards on ancestry, with categories like
human,
demihuman,
non-human. As the DM, I could ensure that there will be at least one of each class group for a balanced party, and most of the ancestry cards would be
human, maybe two labeled
demi-human, and only one labeled
non-human. If you draw the
non-human card, you can play just about any race from the table's bookshelf (or D&D Beyond). Before character creation, players could trade cards! Depending on what kind of genre the DM is going for, the cards that go into the hat can be varied.