You can damage any power steering system by working the wheel back and forth with the car sitting still they are designed to assist with turning the wheels when the car is moving. The loads put on the steering system when the car is stationary are very high and the pump/system can be damaged if you proceed to run the power steering back and forth over a long period of time causing all sorts of issues.
The power steering systems are designed to self burp thats why the cap and the small resevior is at the highest point in the system. If its getting noisy have the fluid flushed with proper spec fluid. Noisy pumps are caused by many things but the most common is old fluid and improper fluid levels - and excessive power steering abuse example would be working the wheel back and forth without the car rolling or sitting still while waiting to make a turn and holding pressure on the wheel causing the power steering system to sit there and work while the car is not moving etc.
Also turning your wheels when not moving creates flat spots on your tires too and puts added wear on the steering components. Prior to power steering these issues were a non issue simply because it was obvious to the driver that trying to turn the wheel while not moving was really hard and really not a good idea.
I have the front up on a jack so, the tires have no resistance on them. The Subaru document I have outlines the engine off, engine on, routine I've been using, but wheels 'unloaded' as you mentioned.
OK, the bad news; it was NOT residual air. I waited 30 minutes or so, looked in the tank - looks OK. Engine off, a few L2L turns, look again - no bubbles or foam. Run the engine, a few L2L turns, turn engine off, a few L2L turns - huge amounts of foam. Still sucking in air.
Good news; Go to Ace hardware with old, flat, almost square cross-section o-ring from suction housing on top of pump. THEY have one! (be sure to mention it's a METRIC application) I have no idea if it's the proper material for automotive PS systems. It's much more flexible that the old one - which almost felt as hard as plastic. $0.80
Bad news; over-torqued bolt replacing housing onto pump. I decided to test the system anyway.
Good news; MUCH less motion/splashing/bubbles in reservoir, noticeably quieter pump
Bad news; couldn't think of a good way to secure the housing with wire or bands so, decided i have to do something about the retaining bolt.
Good news; It came out even though the head was half-torn off!.
Bad news; another trip to Ace hardware.
Good news; they have a stainless bolt that works! And, evidently, the threads were still good so, everything went back together.
I'm still gonna do a few more 'purge' routines, but things seem much better now. And putting some fresh fluid in (valvoline - I guess that's OK?) is probably good as the old stuff is quite dark. I'll probably try to do a complete fluid change in April at regular maintenance time.