Police spotting (junction watch)

Well, they could stick a policeman there night and day to guard it if they wanted to.

That's what's unworkable. And how would the police stationed there catch everyone, e.g. if five cyclists came along at once?

I don't think it's entirely pointless. Without knowing the official reason, it is a very narrow lane, and with the constant oncoming traffic on the other side, mixing buses and bikes there creates potentially dangerous situation, as it's almost impossible for either party to overtake safely.

Of course everyone could just wait their turn and not overtake, but that's unrealistic, so forcing cyclists to take the very minor detour around high holborn seems sensible to me, if it reduces the chance of accidents on that section.
It is a pointless restriction (I wouldn't press on to argue that it's 'entirely' pointless, as obviously the scheme designers had their own points; my contention is that the disadvantages far outweigh the positives), although to explain the ins and outs of why takes a while (happy to over a pint, though). In a nutshell, there is no actual technical problem here that couldn't have been solved somehow during scheme design.

The problem with designing a scheme that you ban cyclists from is that they will use it, anyway, and as their use hasn't been 'designed in', this will often create greater hazards, e.g. like the one you outline--had cyclists been considered, the scheme should have taken a different shape.

The problem, as I mentioned above, is that the default position is not to consider cyclists, and it is quite tiresome to have to argue for exceptions every time, when cyclists should be considered as a matter of course.

By the way, negotiating the Holborn gyratory is anything but a 'minor detour'--it may not be a problem for you or me, but it is a major factor which keeps people from cycling, and negotiating the gyratory will be more hazardous than unlawfully using the bus contraflow (which of course I don't advocate). Remember that these detours all mount up--you have to make so many of them in London that a distance-sensitive modal choice like cycling is seriously disadvantaged by it. If you accept the Holborn detour, you might as well accept almost all of them, anywhere. They are all unacceptable and distort the natural shape of London to seriously warp the modal split of traffic here.