Here's a couple of pictures of CSH #7 on a weekday morning around 8am, near Oval station.
Notice a couple of things about these pictures. First, you'll see cyclists don't restrict themselves to staying in the blue lane, partly because there are so many cyclists they don't all fit. So if this were a segregated lane, you'd get problems with cyclists trying to overtake. Second, and relatedly, there are a lot of cyclists compared to motor vehicles. A brief count revealed that there are indeed more cycles than motor vehicles (ignoring powered two-wheelers).
So when TfL talk about 'balancing transport modes', they need to realise that cyclists are not a tiny minority, and the current balance in terms of roadspace, safety and spending is skewed towards motor vehicles in a way that is totally disproportionate to their numbers, on roads such as this one. Why is it that TfL allow a single parked vehicle to jeopardize the safety of a large number of road users - the most vulnerable - on this road? Why do TfL design junctions with the needs of only one section of road users in mind, and ignore the safety of the others? At peak times, why does TfL think 'traffic flow' matters most for the vehicles that have the most deleterious effect on traffic flow, and doesn't matter at all for everyone else?