Mm, the problem of moving the lid with a bunch of crap on it depends on the sturdyness of the lid.
The lid at my parents’ house is composed of extremely thick ceramic, and has a sort of ridge around the back and the two short sides. This is a heck of a boon, because they keep a bunch of bathroom supplies atop it, and given the age of the house, the guts of the tank need to be fiddled with fairly often.
But the tank in my current apartment… ::sigh:: I can only asume the original tank lid was somehow broken by prior tenants, because it’s flexible plastic and generally looks like a replacement piece. Not a problem, though. We have much more space for storage than my parents’ bathroom, and the lid isn’t really needed as a staond-in for a shelf. All I keep atop it is a glass bottle, blue, with seashells and sand dollars and coral molded into the outside. Goes with the rest of the room’s general seaside theme.
My own gramma never had one of those evil looking little toilet dolls, but I’ve seen them at houses I’ve visited. Poodles, too. ::shudder:: Why not just keep the extra tp in the cabinet under the sink, like a normal person?