There is a lot to talk about here...
I also don't think horses should be extinct, nor cats for that matter, why are these specific creatures extinct? Cats are hunted to death, highly implausible, still an actual explanation, but hunted to death? Cats are nearly as numerous as rabbits, but they were hunted to death? Across all of America? And horses, donkeys, and mules, weren't given any explanation.
I think that equidae shouldn't be extinct, in-fact I really like the sleipnir concept from near the beginning of this thread. Although I don't think they should be the "default" mode of transportation, I don't think they should even be numerous. I'd be fine with them being localized to certain areas of America. I think Wyoming and it's surrounding states would be a great place for them. And while I'm at it, cats could just be really good at hiding in the Fallout universe, unless you want to retcon it and say they weren't hunted and make them just as abundant as dogs. "Why are cats good at hiding? That sounds stupid you rotten-looking child." There's a cat in the middle-east, I can't remember it's name and I don't know what to search, but it's so good at hiding that people didn't even know it existed until recently. And even then, studying them is really hard, we know barely anything about them. I don't see why cats couldn't act like that in Fallout, and if you hate the idea of horses and cats, then mutate them so they aren't just horses and cats.
Although, I wouldn't mind other mounts, and I certainly would not mind vehicles.
Giant birds are something I've wanted in Fallout for a long time, and I do like the idea of them being mounts.
And mole-rat mounts would be very cool. I also think that the 3/NV/4/76 mole-rats shouldn't be mole-rats. Those are pig-rats, except for 4/76, those are mutated naked mole-rats. And also why are pig-rats on the east coast? Maybe Fallout 3 mole-rats could be something else I don't know.
I've been thinking about giant snakes for a while, I even got my dad to paint my concept art for a giant bull-snake. They could be as tall as a sheep, and as long as a bus, and even have the occasional arm/giant claw growing from their side.
More ideas: Giant turtles, bigger goats, bison even, maybe a really fat pig. Also this isn't related but I thought of two more creatures, a rat with a trunk, and a giant butterfly. The butterfly is really rare, and it's body is about a foot long, and maybe it could be considered the "fairy" of Fallout. Cringe? Don't care, maybe a little.
And wind vehicles and energy vehicles are cool as fuck, I disagree with anything else. Energy vehicles should be the most numerous, but harder to maintain. Wind vehicles should be very rare, possibly only craftable, but very easy to maintain. Wind vehicles could also be a bit slower than energy vehicles to further balance it out. I would love a return of vehicles, especially the ones from tactics, the highwayman was okay, but I didn't think it was great. Vertibirds are cool, but depending on the location of the game, I wouldn't like those. I'd also really like the vehicles from Van Buren, and the Frontier, they look really cool.
Some people are saying that vehicles/mounts will ruin the scale of the games, I disagree. It still takes place across North America, which isn't a continent that's known to be very small. Yeah it only takes a half a day to drive from California to Utah, which is possibly a month-long journey on foot, but I don't see how that's a problem. Especially considering all of the wars, wildlife, warped terrain, etc. etc., that will be in your way. Maybe you try to drive from California to Utah, but you're stopped every couple dozen miles by border patrol, and there's no "safe" alternative then going through the border. I know difficulty in travel isn't what people are worried about, but after 43 difficulties, you realize just how far away Utah actually is from California.
I also see people saying this will make society become too developed or something. I personally am a very strong believer that post-post-nuclear is A-okay. It's still the rebuilding of society after a nuclear war. Plus look at Wasteland, post-nuclear still works even when the society is nearly modern. There's still mutants, there's still irradiated areas, there's still tribals/people just struggling, and there is still rebuilding, even after they're at the top. I don't see too big of a difference between Fallout 1's society and Fallout New Vegas', the only reason people point it out is because it's talked about more in-game. In-fact, Fallout 2 and New Vegas are on the same level of social development, but no one ever mentions it. If locations like Sloan, or the Mojave Outpost didn't exist in-game, but were mentioned, people wouldn't think that society has rebuilt too far. Example: by Fallout 2 all of the locations in Fallout 1 are acting like locations in New Vegas, all heavily regulated and contributing something to a larger cause, but we can't see it, and it's not mentioned as much, so people don't think of it that way. You could argue: "We don't see those locations, you are just guessing it's like that!" Which is true. However, I'm guessing it's like that based on how the NCR is depicted in Fallout 2, Van Buren, and New Vegas. And do you assume that those places aren't being treated like they're apart of the NCR? Your guess is just as good as mine is.
I'm probably making a bad argument, maybe the discussion isn't about societal development, but more so technological. Though, that would be a very bad argument, considering every Fallout game has weapons that are able to disintegrate people, armor that's basically just a mini-mech, goo that can alter DNA, and so on. Technologically, and socially, Fallout has been far ahead what would be realistic for a long time, and if it bothers you that much, why not harass Bethesda to make another prequel, or set it in a location that was hit hard, or maybe there's some other force that's caused a certain area to be closer to year zero, just don't re-nuke the wasteland, that's a really lazy, and really bad, idea.