*sprays thread with Lysol to clear the air*
I have a fighting city in that I have mostly military wonders and I fight tourneys, but I still cater Gateway and High Halls of Spire. The logic is easy enough that I can solve them on the first or second try so it doesn't cost that much in goods. Upgrades on buildings only happen once in a blue moon when I unlock those certain techs so goods are piling up unspent anyway. I only have orcs, mana, and seeds to contend with, but haven't found it to be an issue. I've also studied minmax's Spire progression charts and formulas. My conclusion is it's not worth spending my troops in Gateway and High Halls, even if I can win there, esp when the logic is still so easy to cater. They will stretch further in tourney. I'm doing between 6k-9k depending on the tourney so I have massive troop needs for tourney.
With the Lab, the numbers flip. It becomes expensive to cater bc the logic is not in your favor as it's much harder to solve on the first or second try. Therefore, it's not as economical to cater the Lab so I switch to fighting and be done with in one round. I don't know if you're using buffs, whether in the form of expiring buildings from MA or Fire Phoenix, but you will need some buffing to fight the Spire. It's not wise to try bare knuckling it with no buffs. For a lot of us, we're dropping buffs and feeding Fire Phoenix anyway to handle tourney so it's not an added expense for the week. As Soggy says, if you time when you drop the buff buildings, you can use them for 2 weeks worth of Spire. For me, it also works out that by the time Tues rolls around with a new tourney, I'm about to enter the Lab in the Spire so I sync to clearing the Lab with when I'm feeding my Fire Phoenix.