The AK557x ADCs themselves are 32-bit integer already, regardless actual DNR specs.
Basically the floating point approach is just an array of ADCs (or a multichannel ADC) recording at different levels. The old Sony PCM-D100 used a similar approach -- recording two copies at the same time, but with a difference of 12dB. Of course, it only supports 24-bit integer and DSD.
https://www.solidstatesound.co.uk/sony_pcm-d100.htm
While 32-bit float "only" has 25 bits of precision, don't forget it wins 32-bit integer when sample values (yes, sample values, not the overall level of the whole file) are below -42.1442dBFS (7 bits below full scale) and above 0dBFS (integers will clip). Floating point on the other hand always store 25 bits of data within the ~1500dB range. Since no combination of ADC, mic and preamp can achieve 25 bits of instantaneous dynamic range, the floating point approach is much more sensible.
2L for example has a raw DXD vs DSD comparison page here:
http://www.2l.no/hires/DXD-DSD/index.html
Look at the highest peak level of the raw DXD file, it is -12dB, and stored as 24-bit integer. That means the whole file, being integer, only has a maximum bit-depth of 22, and in quieter portions the bit-depth is even lower. In terms of RMS it is about -35dB, so only about 18 bits. Very compressible with flac (~35.5% of original). Typical normalized 16/44 flac (1411kbps) often only has a ratio of about 50-80%.
Not criticizing anything in terms of audibility, just want to clarify the technical details.