The manifestation of an Avatar is not an invasion and neither is speaking with mortals. Hircine doesn't control Werebeast but he can send them dreams as in Bloodmoon or just talk to them like some Daedra like to do.
An "army" of werebeasts would be similar to an army of Dremora. No, the Prince doesn't have direct control, but most would listen and follow orders. That's a big no-no for a Prince to have so much control over Mundus.
We clearly disagree on whether Werebeast have control but they do take orders from Hircine, the ones who want to anyway. The Wereboar from Daggerfall didn't.
But again, there's no information on the wereboar's behavior in beast form (aside that he's hostile to you). Hircine wanted his "child" punished because they hated having lycanthropy. There's nothing to say they weren't still an out-of-control beast when changed, just that they did something about their lycanthropy that strongly displeased Hircine... such as hiding deep in a dungeon away from people, so when they changed there's no one nearby to hunt.
The Werewolves in Bloodmoon kidnapped certain individuals including the PC for the Bloodmoon ritual under Hircine's orders. I don't see why he can't just tell them to leave someone alive every now and then.
A scratch or bite is not a sure-fire way to infect someone with lycanthropy (both in Daggerfall and Bloodmoon, the risk of catching Sanies Lupinus was rather low). That's even if the person doesn't get killed in the process, as werewolves can easily overpower most people, or use a Cure Disease potion/spell afterward. I doubt Hircine even cares to have a large army (not all Daedric Princes wish to take over Nirn, it's mostly just Dagon that does).
The Companions, who in my view are no different, don't seem to have a problem infecting others with their blood. Other Werebeast could do the same for the willing.
That of course requires a willing "victim" and someone who's willing to turn other people. Given the normal state of lycanthropy, with the need to change and kill, it's not something people would normally want to give, let alone accept. The Circle doesn't have a need to change and kill, though, which gives them better PR (yet it's still not something they're public about).
Werebeast are NOT Daedra. Nor are Vampires. They were created by Daedric Princess but are not Daedra themselves. They were changed, similarly to the Dunmer who were cursed by Azura, same with the Khajiit or how the Orcs were changed by Boethiah. They are essentially different races if you want to think of it that way.
Though the Dunmer, Khajiit, and Orcs weren't created. They were Chimer, Forest People, and Aldmer that were changed following a huge cultural shift. Werebeasts have a completely different mindset while in beast form compared to their normal form, and constantly change back and forth. It's not a cultural thing.
Vampires were created by corrupting a person and changing them, so aren't Daedra. But Hircine can make werebeasts:
Confident, but knowing Sheogorath for a trickster, Hircine secretly bred an abomination in his hidden realm. An ancient Daedroth he summoned, and imbued it with the foul curse of lycanthropy. Of pitch heart and jagged fang, the unspeakable horror had no peer, even among the great hunters of Hircine's sphere.
In the third year, on the given day, Hircine returned, where Sheogorath leaned, cross-legged on a stone, whistling with idle patience. The Prince of the Hunt struck his spear to the ground, bringing forth his unnatural, snarling behemoth.
http://imperial-library.info/content/16-accords-madness
It's reasonable to assume Daedra such as these were the ones to first infect people on Nirn. And I like to think a person's body being taken over by a Daedric spirit brings in a nice mystical element to it. Note how the cures to lycanthropy involved forcing your lycanthropy onto someone else and killing them (Daggerfall and Bloodmoon) or by separating a beast spirit from you and killing that spirit (Skyrim).
There is Sinding, though he had issues, also had control enough to transform and escape inprisonment and then to hunt down his hunters.
Sinding killed the girl, then later killed a group of hunters. In normal form, he doesn't want all the killing and wants to be left alone to live a normal life, but in beast form he's all for killing. He just doesn't want to kill you because you helped him and you were a werewolf at that point (given the cursed Ring of Hircine that makes you change at random).
Someone with lycanthropy can change into beast form once a day, that's not a Circle-only thing.
If he/she had not taken it upon themselves to kill (while still disobeying Hircine) then they would have died and there would have been no need for Hircine to send the PC on the quest.
In Daggerfall, you did not die from not killing. You were just severely weakened such that you'd be likely to die if you ever ran into anything that could pinch you.