I would agree that it might be a disadvantage for women, but conversely I would just make an effort to ensure there was _someone_ else with us, male or female. So instead of drinks 1:1 outside work, or a 1:1 meeting, It would instead be three people which mitigates both parties liability.
I am a senior engineer, not a manager, but if I were a manager one on ones would be necessary, I would attempt to have HR in each 1:1 as an ass-saving measure anyway.
But then again, I believe I would be a poor manager so I don't wish it on anybody.
As an aside, it's always nice to hear someone who recognizes they aren't a good fit to be a manager. I'm not sure I would be good at it either but it seems that even people who very obviously don't have the personality for it tend to jump at the opportunity.
I speak from experience from being around vindictive people.
That doesn't sound realistic, for a couple of reasons:
1. 1:1 meetings between a manager and their staff happen on a regular basis, e.g., weekly. If HR had to attend each of these meetings, they'd never get their own work done. (HR's job is to cover the company's ass, not yours.)
2. If your employee walks into your office for a 1:1 meeting and finds someone from HR there, they'll freak out because they'll think they're about to be fired. (That's a typical situation where managers call HR for backup.)
As a small counter to your post though, I've read some articles recently talking about the importance of general social networking and one on one mentoring in some professions with the point being made that if men in power in these professions adopt a stance of not being alone with women, this could impact women's ability to progress professionally compared to their male peers. I think it's important that if you adopt such a stance, and are in a position of power, that you find ways to mitigate the unintended effect it may have on women.
I actually have a male friend who was accused of harassment by a female subordinate that was later decided in his favor. Being gay, happily married, and from what I know of him a very good employee and boss, surely helped his case. After this incident he stopped all outside of work one on one meetings, but he did so with both men and women so no one is adversely impacted by his choice.