Infeasible for a government would mean it is sufficiently expensive that it is not politically popular to spend that much money on public bathrooms.
Also, Buc-ees does not offer free bathrooms in urban, dense areas with higher proportions of mentally ill and drug addicted populations, so that comparison makes no sense.
I used Buc-ee's as an example because they're famous for their clean bathrooms. But there certainly exist clean bathrooms in urban areas. I'd venture to say that those aren't all in high-end establishments that exclude any "riff-raff". It's possible to find clean toilets in urban McDonald's or Wal-Mart; maybe not all of them, but certainly not none either.
And regarding expense on public bathrooms:
* San Francisco spent $1.7M on a single toilet
* Seattle spend $5 installing 5 toilets.
* NYC's public restrooms routinely cost $2M-$4M
Now, those are building projects rather than ongoing operations. But it shows that governments are willing to spend absurd amounts on toilets.
I don't know exactly what the problem is, but there's something about government (mis)management in the issue.
Sure, but why is it that government-run institutions are (we're being told in this thread) uniquely vulnerable to the problem? Why isn't it happening at Buc-ee's or at McDonald's in the same degree?
