Because the world is way to large for you to only be able to ride around on a regular mount. SW:TOR and GW2 have some kind of portal/teleportation system wherever you are in the world (more or less), while World of Warcraft had its flight paths. In order to get from A to B, you either had to walk on foot, ride a ground mount or use flight paths, unless you were able to be summoned/teleported that is. It took time getting from A to B. Players wanted a faster means of transportation, and flying mounts surely was the most fitting for a fantasy world. I love having a flying mount, even though I would've been able to work without it in many cases, it is still a lot faster. Just think of the time you save by flying from for instance the Jade Forest to Shrine of a gazillion moons/stars instead of riding on a regular mount there. It is a huge amount of time saved. You would've cried if flying mounts were removed.
I remember Blizzard mentioning having mounted battles possibly implemented a couple years back. And I do remember that idea being scrapped shortly thereafter. Battles in the air would be awesome, but I doubt that will happen anytime soon.
World PvP is still there, but there's no reason for anyone to actually go out and fight over places like Southshore or Crossroads anymore. I posted a long long post about this matter a couple years back, in regards to bringing world PvP in the form of objective based battles placed all over the world. It is a war between the Alliance and the Horde after all. A battle we rarely see anything of. A battle between the factions should consist of hundreds on each side, and CCR would help this idea further immensely. But meh. We're getting more battlegrounds, which is boring.
I liked Wintergrasp and Tol Barad to some degree, but you did not feel attached to it. If that same battle were to take place in for instance the outskirts of any of the major cities, you would get that feeling back instantly. Who wouldn't fight for the survival of their main capital? Anyway. Back to flying mounts. There's nothing wrong with it. The thing that is bad and should be improved is the way people would be forced to go out and do stuff. Ganking people during their daily grind isn't world pvp. It's just lame. Do anyone at all remember the awesomeness when people gathered hundreds in order to take on for instance Crossroads? The whole of Barrens became a battleground! This was not due to how awesome Blizzard was, this was due to the community. The community was the one who marched out there in order to have some world pvp, not Blizzard forcing you to do so.
You have battlegrounds and arenas now. All of which gives you more in regards to actual rewards than what world PvP does. The honor gain is laughable compared to the one you get during a battleground, which often lasts less than 10 minutes. The community isn't after community based entertainment, they want rewards. When something do not give them an reward, they do not want to do it.
Mind you that I am, and has always been, on a PvE server. We had to make our own world PvP. Before Cross-realm battlegrounds, you were fighting the opposing faction. People you knew. People who might have ganked you a million times while you were leveling. It was personal. It was fun. In battleground, you met the same people. I were part of the realms finest teams back in vanilla. We absolutely annihilated the Horde, unless we met a certain team whom we always had lengthy battles against (Fusion ...). When cross-realm battlegrounds were released, the teams sticked together and owned pretty much everything. But the fun was lost. You did not fight those you knew. Only random people of X, Y and Z realm were fighting against you. There was no tactics involved in the fight against you. It became boring. And so the team slowly dissolved. Why? Because you did not need to actually have a good team in order to win anymore.
Back to world Pvp. It died at the start of TBC. And I wouldn't say it was purely based upon the fact that people obtained their flying mounts, I would rather say it was because of the way the community started to grow into the idea of everything being rewarding. Halaa in Nagrand gave you great rewards. Throughout most of TBC there were battles going on. Now? It's more or less dead. Wintergrasp was a giant pvp zone. People fought in order to get a raid dungeon and items. This zone was even scaled down in the sense of number of players able to attend the battle at any given time. Tol Barad, I did not personally play this pvp zone a lot, due to the fact that I were more or less inactive throughout the Cataclysm, but again it was the rewards driving people. Who would've fought in either of these zones if there weren't for the rewards? People rarely cared about the dailies there.
So no. It was not the flying mounts who killed world pvp, it was the community and their mentality. If I were to start a Cross-roads world pvp team right now, I doubt I would see any high level Hordes attending later on (I am Alliance).
Oh, one more thing. Who have their /world defense channel turned on? Oh, you do not know what it is? Ok. How do you know if a fight breaks out in location X if you do not have either /local defense or /world defense enabled? Trade chat? It's all because of the community. Rewards, rewards, rewards and some more rewards. That is all the community wants. If there's no rewards, then there's no reason for them to do it either.
I still cannot see why Blizzard isn't increasing the honor gain in the world, something they reduced by a lot a couple years back. Honor isn't really what's driving people, but if it did give you a large enough incentive to actually go out there, then people would do so. Adding in achievements, quests, dailies, phased areas, organized yelling by town guards or something that is attached to the world, people might have a reason to do it. Do you see flying mounts being part of either of these? Flying mounts more or less only fixed the flaw where higher level people would gank whomever they found in an area. People are often to scared of trying to fight someone who is actually their own level, unless they actually know what they're doing.
I could've continued writing for hours, but I really need to get back to writing my report.
My final sentences would be the following; Fix the community and you'll fix a lot of problems. Fixing the community is impossible. Therefore, the game will be broken in most peoples eyes, because they have expectations Blizzard cannot fulfill.