Pro: A larger volume of water will be PH stable over a longer time.
You will not need to check on it as often.
You may be able to get away with reservoir changes for up to 10 days.
Con: It will require more nutrients to reach your desired PPM $$$
You will not be checking on it as often and may miss a problem that harms the plants.
Plants in rapid growth may deplete a nutrient component to levels that will slow it down. This is the main reason for weekly reservoir change.
Having a separate tank for mixing is much harder and mixing in a live system is dangerous.
You will have a lot more waste to dispose. I use mine in my yard and 3 gallons twice a week is a lot for our yard.
When I was using 36 gallons a week for 6 plants it was very expensive for nutrients and I had to flush a lot of waste down the drain. This is not environmentally sound.
I am not saying you cannot do it, I just want you to be aware of the facts before you get into it.