It IS a problem as it is too frequent and forces the player to do the Dawnguard quest when they probably don't want to suffer the Soul Cairn a second time. And the vampire attacks happen straight away, unlike the dragon attacks where you could stop it from happening by just not collecting the dragonstone.
But if you're fine with the frequency, then surely you'll notice the AI problems where civilians (some of which aren't even armed) will charge the vampires mindlessly, getting themselves killed. There's also the problem where vampires will find that farmers and blacksmiths are a bigger priority than a Dragonborn.
You have to go a lot further than just collecting the Dragonstone to be afflicted with never ending dragon attacks. Collecting the Dragonstone got you one scripted dragon attack, and you had a lot of help killing it, or could even just wait for the Whiterun guards to kill it. Yes Skyrim has dragons, the few with set locations are big enough and obvious enough to avoid if you do not want to fight them. You do not get random spawning dragons till Alduin wakes them.
I noticed no AI problems, most NPC's have always defended their towns, as those who did the main questline would know from the Dragon attacks. And those who ran still could die anyway. And a few vampires are a lot easier to kill than a dragon. Whether it is a dragon or a group of vampires, they are attacking the town, so why would they only go for your character? They kill whoever is closest. If you downloaded the DLC presumably you were intending to play it, but I saw no sign of being forced to start the Dawnguard quest. My only high level over achiever who had the vampire attacks straight away could have easily just killed them and continued what he was doing, he had an extremely high rate of random events, so adding vampires into the mix was hardly going to be that much of an inconvenience. But since he had done all the questlines he was the character the DLC was mainly for anyway. My other two characters continued with the main game and never had to worry about vampire attacks on towns, Aussie had to join the Dawnguard to get them. So how you play and what you have done has a big effect on what you get with the DLC.