The reason for it, i.e. the reason you believe this, is likely confirmation bias I think. There are poor-quality restrooms in Japan, but whether they are 'public' or 'private' has little to do with it. You can go to a city office, or a police station, and it's even odds what you'll find. Likewise, you can go to a shopping center, and also find examples of both, and I will say that personally some of the worst restrooms I've seen in Japan have been in older shopping malls. Train stations will run the gamut, which doesn't give much evidence either way, regardless of whether you consider those public or private. Parks tend to be lower quality, but there are exceptions.

Instead, what you'll find is that it tends to depend on the age of the building. There are seem to be very few examples of low-quality restrooms built in Japan in the last 10-15 years, regardless of who paid for the building.

Builders get kickbacks from the manufacturer of these smart toilets if they choose to put one in when their client doesn't specify what toilet they want.

Probably not the only reason, but it definitely contributes.