Then the question is whether you're going to keep them from doing just that, because in my experience, most players treat logistics puzzles as a Gordian Knot; cutting through it as quickly and efficiently as possible to get past it.
I don't think you want to keep them from doing something, you want to incentivize doing something more fun. You could cut up the statue, but maybe it is worth significantly more in its complete form because some very wealthy buyer (a dragon?) will pay a premium for this art piece. Maybe it is a magical artifact instead of just cash, and you can't keep it and cut it up. Or, maybe hiring all the people you need to cut it up and move the pieces invites all sorts of trouble.
Sure, but some versions of the game and even some 5E campaigns make monetary treasure important to advancement or in-fiction aspects of the campaign.
Teaching players not to expect loot and to steal from random NPCs and field strip corpses to scrape gold together for their needs.
No, they expect loot, they just don't expect boring loot.
Self-described 'pain in the butt' is honestly worse than boring like +x blandness.
But that isn't the players' responsibility. If they come up with a way to do things quickly and easily so that they can move onto the next thing, it's not their responsibility to discard that option in favour of something that will keep them there longer.
