It makes sense to turn them off when they are not needed, of course.
Control transformers might be about 250VA. That's roughly an amp at 240V, a bit less at 208, or a half amp at 480. (less if smaller)
They may draw as much as 5% of that when unloaded, so 0.05A at 240V. Of that, only maybe 25% is "power" current due to the low power factor.
If you were paying 40 cents per kW hour, then on a kW basis you would pay for about 2.2 kW hours per month, or about 90 cents per transformer. It doesn't do anything for you, but it's not a ton of money. Might take a lot of months to pay for a new contactor. A disconnect may be cheaper in months to payback.
I'm estimating high, so if a transformer is costing you more than that per 250VA of capability @$0.4 per KWh, you are being charged on a different basis (which would be normal for 3 phase service).
Any transformer will have a rotten power factor when not supplying a load, possibly as low as 0.1 or lower. If nothing else is drawing power, then that is your facility power factor when the place is closed, and the powerco may hit you with a surcharge.
A 480 to 208/120 transformer might cost many times the amount calculated above, based on lousy power factor, because it will draw a lot more idle current. Any old-style fluorescent fixtures connected to it won't help at all either.
You can fix that, if the transformer cannot be shut off, by connecting enough capacitors to raise the power factor to whatever the powerco says is their minimum. That has a cost also, due to parts and install charges.
If you have a new type meter, it may give you the information as to what kW and kVA you are drawing. They have a series of display readings they cycle through. Sometimes they say what the number is, or your powerco may have a "how to read your meter" information page on the website, etc.