Should larger pots sit in the water?

I have been growing in DWC for a while now using a 6 inch pot, however my plants have been getting quite big and the roots are breaking apart the pots and I feel like possibly being strangled by it so I purchased some 10 inch pots. Normally I keep my water level about 2 - 3 inches below the bottom because when I first started out I killed a couple seedlings by having too much water in the buckets, however I noticed that the 10 inch pots are roughly twice as deep as the 6 inch pot and if I had the water level 2-3 inches below the pot I'd have no water left!

When you guys run these larger pots do you let the water level rise above the bottom of the pot or do you just have deep enough buckets that it's not an issue?

If your water has a proper amount of oxygen I don't see there being any problems with some of the pot being submerged. with dwc as much of the root mass can be flooded as u want. More roots under water is more surface for the plant to feed