If given a problem with everyday objects are they capable of at least rarely responding with useful novel solutions? Even rare anecdotal evidence might be interesting if it gives better chances than the monkey typing
They are "capable", but only by chance. If you generate millions of random sentences in a human language then some of them would express some "useful new solutions". LLMs would have a higher chance of this happening as they generate sentences that are statistically more probable and therefore more likely to represent a coherent thought, but this would still be a chance.
The good thing is, you will probably remember that one good one and forget about unsuccessful generations; just like how a gambler will only remember that one time he won something, and never talk about most of the time he lost.
The same is usually true for "human" inventors. I mean not forgetting or gambling, but having many unsuccessful attempts with probably a single good outcome. Recently read "Reinventing the wheel" by Steve Kemper (also known as "Code name Ginger" about Segway development), the funny term for this from Kamen himself was "frog kissing".
