It's still a better idea to keep a low profile than to flounce around with an antique pigsticker loudly expositing about your origins and motives when there's a world wide security network and random civilians who can recognize you. Hell, Vergil is such an incompetant boob that this stupid behaviour nearly costs him everything when he had to stab that informant with a throwing knife.
That's quite a stretch, considering they obviously didn't walk into an area rife with security cameras, and as mentioned before Vergil isn't someone to recognize, he's nearly a random Joe Shmoe in a fancy hat. Plus, he was talking about his origins in a clearly empty space with no cameras, but somehow to you it was foolish of him to do so there? C'mon dude, you're looking at this far too much from a perspective that everything everyone does in this is wrong. It's pretty obvious Vergil knew what he was doing when he talked to Dante in that place, and one random-ass demon collaborator out of earshot at the end of that scene wasn't going to gleam any grand secrets. As for killing the guy, we don't know what happened after that, wouldn't it be logical to think they took the body away...? If you had any capability of thinking that they could do something right, wouldn't you think they would cover their tracks?
...that really makes no difference whatsoever. Lillith was still a known arch demon, Vergil still wanted her dead and had access to the resources necessary to kill her for years before Dante showed up. If all it took was one punk with a gat putting a hollow in her temple while she's standing on her little balcony a halfway competent terrorist could have polished her off in an evening.
They also knew Bob Barbas was a demon, and probably several other people. The big point is that if you're trying to seem like the good guy, you certainly don't want to "march a kid strapped with explosives into her club to give her a hug," or have a "punk with a gat put a hollow in her temple." They're already struggling with a blow-hard on TV calling them terrorists, why would they actually want to stoop to that level :/ Plus, Lilith was
still not a priority target until her value to Mundus was discovered.
He'd still have a city full of dead lieutenants and no means to control the populace other than "debt". He'd be forced to leave his tower and clean shop eventually, seeing as his awesome godly powers don't seem capable of destroying the man who killed his family, even if Dante was using his power to shift too-and-fro between Limbo and Reality that he just-this-second-made-up to protect him.
Did you not see how difficult it was to get into Mundus' office where the Hell Gate was? They needed someone with a floorplan just to navigate through most of the tower's dangers, and Mundus had no reason to think Kat or anyone else knew what it's Limbo floorplan was like, and it also involved Vergil taking out security systems without drawing attention, so he was a completely unseen factor as well that Mundus didn't have any clue to account for. For all intents and purposes, the Hell Gate is pretty friggin' secure, even for the Nephilim he feared.
And people still looooove Kyle Ryder and think of him as a savior, and there were more people to Mundus' ranks than just Poison, Barbas, and Lilith, those are just the ones that were deemed important enough to hit (and be in the game's story). Hell, even Lilith wasn't important enough to target until they found out she was carrying the demon spawn and they could potentially trade her for Kat.
Not sure what that last bit is about...
I think what Martius is trying to say that there's no reason why Mundas couldn't grab Dante by the face and drag him into Hell for an eternity of inescapable agony and torment, or just punched off his head. It was a huge logical leap to presume that he'd punt him out of the building first, no matter how angry he is. It would have made much more sense if Dante physically lured him out of the building while taunting him.
And that very well could have been part of his plan - get Mundus riled up enough to the point where he'd easily follow Dante wherever. However, Mundus got super-****ed and just bull-rushed them both out of the building in a blind rage instead. People get angry and do stupid things without thinking of the consequences, but Mundus also could have done it in an attempt to
not have Dante near the Hell Gate. And really, huge logical leap? I wouldn't think it that unrealistic of a reaction to a guy taunting someone about their dead child.
And again, what did it matter to him? He was immortal at the time, he thought he was safe.
There's several options he could have gone with, but in the end he decided to rush Dante out of the building in anger. You're looking way to deep into the could-haves without actually taking into consideration why what happened, happened. Mundus got angry over a punk making fun of his recently murdered heir, and made a grave mistake in leaving the Hell Gate exposed, but to his credit, Mundus
didn't know there was someone else there that would close the thing and leave him vulnerable.