I'll push as far as I can every week, considering the time I have available and my inventory. I go for all the prizes, personal and FS rewards at the end. Every little bit helps grow my city. My priority is to get in 5 rounds for all the KP.
I don't understand why anyone is worried about burning supplies and goods? Those are cheap and that's what they are for, to use and spend. I view all the inventory items as different types of currency, each with a respective "value" . Some items like blueprints and RR are worth a lot more than others. Supplies and goods are at the bottom of the list and should be expended and used. No reason to hold on to something that doesn't hold a lot of value and easily replaced for free.
For caterers, you are effectively trading supplies and goods for tourney rewards. That's a fair trade in my opinion, because nearly every reward is worth more than the supplies and goods. Same with fighters, but instead you are "trading" troops for the rewards. Again, troops are equal to supplies+time, so that's a fair trade. If you climb the Spire weekly, get all sorts of great stuff in exchange for basic goods. Fair trade in my opinion.
All the rewards can help you grow your city at a much faster and more efficient pace.