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@clubman
First, a correction: The Ballon gradient is not 15%, but 1 in 15, more like 7% - as you may have noticed I am far from fully metricated.(now corrected)
I don't think there's any problem with sustained climbing on fixed. My impression is that on gears one always seems to need a slightly lower gear than would be necessary on fixed. Of course this may be pure prejudice on my part.
A couple of years before the Ballon trip I rode up the Col D'Aspin ( about 1400 metres ) and the Tourmalet (2100m. approx.)on gears using a 32T inner ring and a 23T bottom sprocket. On the Aspin I don't think I went below the 19 and everything seemed fairly easy, although pretty slow. The Tourmalet proved a completely different proposition - perhaps the first climb had taken more out of me than I realised. About a third of the way up I was firmly on the 23, and by La Mongie (three quarters of the way) I was having serious doubts about whether I was going to make it at all. Altogether I'd probably done 25 miles, but it felt nearer 100. I don't know if I could get up these climbs on my 43 x 22 - I'd certainly like to try.
Why would anyone want to do this? If motorcycling is mainly about going round corners, cycling is mostly about climbing - driving a car is more about trying to keep awake.