Your assumption is incorrect.
Levels, Curves, Hue/Saturation, Channel Mixer and Color Lookup all work correctly in 32 bit/channel Floating Point Linear Gamma
32 bits/channel is not an ideal working space as there is no monitor which can display the entire 32 bit range. Instead the visible range in the preview is clipped and can be adjusted for which part of the range is visible using the 32 bit exposure slider at the bottom left of the document window. That does not affect the image, it just selects the range being previewed. 32 bit linear gamma is properly colour managed but is best reserved for HDR images and the output of 3D scene renders. If they are going to print though they do need conversion to a 16 bit, or 8 bit gamma encoded colour space. 8 and 16 bit both share the same range but 16 bit splits the image into more steps. That conversion is called tone mapping, and it involves selecting which parts of the range will be converted, which will be compressed and which will be discarded. If it will never be printed and will be passed within a studio environment (e.g. for CGI) then OpenColorIO settings are potentially a better model than ICC and have been added to Photoshop in the recent release.
In short, 32 bit does not 'improve the colour management experience' and in some ways makes it more difficult to manage (even a so called HDR display cannot show the entire range). It is though appropriate in specific use cases where Photoshop is in a workflow for HDR or CGI.I would though advise working in 16 bits/channel, rather than 8 bits/channel, on a day to day basis and working with a 10 bit/channel monitor (also known as 30 bit monitor). In reality, outside those specialist use cases, a high quality 10 bit/channel monitor with a high uniformity across the panel, and the capability of monitor colour management by uploading LUTs to the monitor itself, will improve the day to day experience, and accuracy of colour, for any user.
Dave