I assume you're talking about software engineers, because in every office I've worked in the toilets have been absolutely filthy by mid-morning.
At my current place there are boot marks on top of the toilet seat that have been there for weeks, put there by one of the 10 people in the company.
I think we can just apply the broken windows theory here. If whoever's responsible for the toilet doesn't demonstrate that they care about its state of cleanliness and repair, the people using the toilet won't care about that either.