Thats a spicy take. You know the seat being down is more than convenience, right? It's extremely unhygienic to flush an open toilet let alone the dangers of small children falling in. I recognize a public space is less likely to have a child small enough and unattended to worry significantly about.

We live in a society and all that. Personal responsibility only works if you err on the side of caution. If there is a default setting to a toilet seat and cover it would be down and closed. Otherwise, why put one on at all.