There are various type of soaker hose. It is important to know pore size and size of openings either for water or air release. Some soaker hoses produce very small bubbles; actually too small of bubbles where the pores quickly clog with bacteria, slime, and algae. Cleaning soaker hose is a high maintenance way of diffuser aeration.
Water running through the soaker hose will not aerate unless the hose is out of the water, not submerges. It takes pressure to push water out the soaker hose. Pressure costs money and is likely more expensive than creating air pressure.
