Well no, lets be clear, nobody is "lazily insisting there isn't a problem" and I don't think anybody has denied that some people cycle badly (RLJing, pavement cycling, etc).

There has, however, been a quite reasonable disagreement as to the scale of the problem. Opponents to the licensing of cyclists debate that the scale of the problem does not justify that level of response. I've personally seen no evidence here, or elsewhere, to convince me it is a rational, effective and justifiable response to 'the problem'.

I understand your statement that, as a pedestrian, you are not worried about cars on pavements so I also understand why you focus on pavement cycling. I know (lies, damned lies and) statistics aren't everything and personal experience does count too but, on face value the stats don't really back you up.

I'm conscious that the links I'm about to post below are for a cycling organisation but the data they reference is independent and, in my opinion thoughtfully (rather than lazily or creatively) presented.

Pedestrians - pages 2 and 3 particularly
Cyclist Behaviour - also has a section on the licensing subject