From an artistic standpoint, I'd think you'd want a new director to go with a new actor, to emphasize that it's a fresh start, a clean break, "not your father's Bond" etc. As evidence of how this can work, we have OHMSS, which still stands out as a very unique entry in the series not only because it's Laz's only outing but also because it's Hunt's only time in the director's chair, and his style is very different to what went before and came after. If EON had gone for "business as usual" by returning to Hamilton, Young or Gilbert, I'm sure it would have been a very different film. Possibly we'd be a lot less willing to overlook the rough edges, like Lazenby's inexperience, if the film overall had been a cookie-cutter Bond flick; I think it would've added to the feeling that George was just a "stand-in" for the "real" Bond, instead of creating the more favorable impression that they were going for something boldly different and special. Even if it's not 100% successful (and some would argue it IS), you just have more admiration for them when they're wiling to go outside the comfort zone and take risks.
Then again, it's worth asking whether the producers really went into it knowing what Hunt was going to give them. After all, he was new to directing and it's possible they just expected him to follow the template set by the predecessors he'd worked under. Maybe the fact that he was never asked back suggests they weren't as crazy about his style as some of the rest of us are.
From a producer's point of view, It is a business after all, and sometimes continuity is comforting. After 12 years (!) of Moore, EON was going out on a limb with whomever they chose to replace him (even if half the world did think Roger should've left a film or two earlier), so it kind of made sense to put Glen in charge of Dalton's debut. By that point, Glen was pretty much a Bond-making machine, so even if Dalton had proven to be troublesome, everything else was a known quantity.
The interesting one, for me, is LALD. After the great success of GF, I really found Hamilton's DAF to be limp, lazy and uninspired, but somehow when Moore shows up, Hamilton's got his "A" game on again. Everything's a little tighter, more lively, more energized, adding to the feeling that youth and freshness has been injected (in spite of Roger actually being older than Sean).
Regardless of what we might want, I suspect the next Bond will be introduced with a new director and a new "spin." The Craig Bond, for me, is almost entirely different from the "Classic" model Bond (or Fleming Bond, but I'm not getting into that argument), so making the next actor follow his lead would mean asking him to do a Craig impression, and that would be as big a mistake as, in the old days, asking an actor to imitate Connery. The next guy should be allowed to go his own way, and part of that should be getting a director who's sympatico with his approach.
Plus, given that Mendes is the first director to do consecutive Bonds in 26 years (!) I think it's pretty obvious what the odds favor.