I can only speak to the Bar, but I think the skills gained from a PhD overlap significantly (albeit not completely) with the skills needed to be a good lawyer. The points that were relevant in my case were (1) the fact that a PhD requires the ability to work independently (2) the fact that it is invariably a test of endurance (3) the fact that it requires you to synthesise a large pool of data (4) general academic ability, and (5) writing skills. Per se it is less likely to provide direct help with things like client management skills or oral advocacy. To that can probably be added the leadership criterion that you raise, although some graduate students do take leadership roles organising conferences, subject groups etc.
So, summarising the above, I think the skills I gained on the PhD make me a better lawyer. But that's not to say that I think doing one was necessary to my career. I also suspect, without having information to that effect, that some people do prefer candidates 'fresh' from undergraduate/Master's level study. I imagine that such people are in the minority, but I do think they probably exist.
In summary, I think the impact of having done a PhD is probably less than one might imagine, albeit probably a net positive. The other side of the equation is the time and cost of doing one. Since you have funding, then it's really a time question. If you really want to do it, and you think you'd always regret not doing one, those are strong reasons to go ahead. But I wouldn't proceed on the assumption that it's a necessity, and I would bear in mind the (hopefully remote) possibility that, for all that it may open some doors, it may close others. But that's true of many choices.