Cosmo,
To be fair, I think AirRabbit is advocating a balance between numbers and execution. One should be confident in visually assessing the manoeuvrings required, but a solid starting point (the predicted numbers) is pretty essential for a reliable outcome too. However, it is certainly the case that some cirling approaches are so compact, that if the initial path isn't pretty much spot on, it will probably be a go-around and so numbers can be crucial to success.
AirRabbit,
The fact that a "circle-to-land" is a visual maneuver appears to be completely disregarded and replaced with a dependence on altitude and stop-watch timing to determine when to turn to land. It's a VISUAL maneuver. It has nothing to do with blindingly flying until a determined number of seconds has ticked by - and then doing something else - likely just as questionable.
I suspect, if this is the way people approach a circling approach it is because they only ever perform the act in the sim, where the visuals are not panoramic and actually require a calculated flight path such then when the runway is again sighted half way around base it is roughly in the right position.