BHG was perfect before the mercs were nerft down. - after that, every scum went to join the BHG faction and the reputation is now ruined for a long long time. - one must be ashamed to be BHG, even if you try hard to RP.
when you nerf the BHG to smaller ships - you have two problems...
- a whole line of ships is gone
- the same that went from mercs to BHG will join the next best faction ( zoners / junkers )
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Not necessarily, since only the BHG and Mercenaries can justify (?) operating (PvPing for that matter) largely in any corner of Sirius. While Zoners and Junkers also have a broad Zone of Interest, their operations are very different from that of the Mercenaries and the BHG and wouldn't be so attractive to the kinds that gave the Mercenaries and now the BHG the bad name. But I understand your point. So, let's try and see it from a different perspective.
The biggest issue is that those ships that were supposed to be operating in the Border Worlds aren't doing so. The whole debate about "which path are them (the ships) supposed to take to reach the Border Systems" becomes kinda moot when the only thing those ships do is keep trolling and loitering inside Core Systems (some don't ever leave to the Border Systems anyway). What I don't exactly understand is why you're pointing out Liberty as a starting point in the first place. Aren't those capitals built/sold in the Omega-15 system? From there they can take a direct route inside the Border Systems to Kusari (only "valid" entry point to Delta). Well, if Kusari is blocking those ships from passing through to Delta, then that indeed becomes a problem.
How about petitioning a jump hole from from 56 straight to Delta or at least leading to a reasonable route, then? It would make a lot of sense for the BHG to pick a guard system from which they have a direct link to one of their main Zones of Interest.
House systems wouldn't be so resistant to the BHG (specially their cruisers and up) if experience didn't show that those warships are being employed inside House territory, putting House security in check.
EDIT:
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If I correctly understand the old Merc situation, the problems were that you had Mercs buying any ship they wanted (including the Nomad BS) and slapping any equipment on it that caught their fancy. I don't believe that the current problem with BH BCers is quite that dire. Most seem to at least understand that BH use the gear allowed for BH. I did spot one fellow a week ago with some Kusari turrets and suggested to him that they were probably not all that kosher, considering Kusarian attitudes towards BH. He left to change his turrets after our conversation. Proof in the pudding that BH capship pilots are willing to take constructive criticism and make adjustments.
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Yes, Mercenaries had the additional issue of displaying an assortment of combinations. From the standpoint of someone who enjoys the faction (or the ID for that matter). The 4.84 nerfing was a very welcome one to the Mercenaries. I figured that to the people that enjoy the BHG as a faction rather than its set of ships it would be as welcome.
Even though the fact that Mercenaries would use anything in 4.83, the main issue was their employment of the ships. Much less than the BHG, there was no RP reasoning for the Mercenaries' capital ships. They were just big pwnmachines. The BHG, on the other hand, has a very well defined reasoning behind their capitals. Problem is that instead of this reasoning serving as a strong guideline for the role to be portrayed by the BHG players that chose to fly their capitals, it merely serves as an excuse for those ships to exist and for the players to own them. As a result we have a Sirius wide police flying battleships.
This is not the case for all players, but it's the case for the vast majority of the ones using those ships. At least the ones who have motivated House governments to be resistant to them.