What seems to be the problem is that everyone, whether they needed step free access to the Underground (or indeed wanted to use the Underground at all) were being directed to the 533 instead of the quicker alternatives of walking across the bridge or using the Underground or mainline stations in Putney.
I thought TfL's suggestion for Roehamptonites was the 265 to Putney Bridge, whose frequency has been increased for that reason - not much good if Hammersmith was your objective though.
Hammersmth Bridge was closed for 17 months in 1997/98.