Yes, that is correct. There is a small loss of bromide from water dilution and from some bromine outgassing and from some combined bromine with organics getting caught in the filter, but you shouldn't need to use only tabs for bromine. The main use of the tabs is that they slowly dissolve so are automatic dosing.
15 pounds of bromine tabs is equivalent to 10 pounds of bromine which in 22,000 gallons is 54 mg/L (ppm) bromine so over 7 days that's 7.7 ppm per day which is a bit high. More normal usage would be around 5 ppm or so per day. 7.7 ppm bromine per day is equivalent to 3.4 ppm FC per day so not unheard of for daily usage.
You might try seeing if using CYA in the water helps reduce the loss rate. If you want to experiment first using a large bucket of pool water, you can do that. At least with the bromide bank you can use chlorine to activate more bromine and that will be less expensive than using bromine tabs, but using most chlorine sources would require adding chlorine every day or two. It might be possible to use Trichlor tabs in a floating feeder, but you can't use them in the bromine feeder as its designed for bromine tabs.