Why do my stainless steel fry pans always develop a residue?
I use stainless daily, and they are pans I have had for almost 20 years.  The outside of my pans look like crap, but the inside looks like your final pic.  My tips are: (1) Reduce your heat a bit when you can, as high heat will polymerize the oils in your pan, creating the coating that is difficult to clean.  (2) Make sure you are using proper cooking techniques, particularly when it comes to using the correct pan for the job, and deglazing. Also, your pan does not have to be smoking hot before you add oil or ingredients.  Be gentle. (3) Clean pans right after use, and when you see a hint of polymerized oil (the brown haze) work hard to get it off (it's actually not so hard...just takes some effort, and sometimes some scouring powder and/or pad).  Any residue you leave behind will worsen with time.
The pans pictured can certainly be cleaned up. It will now take some elbow grease, but it would be in your best interest.  Use a scouring powder with just enough water to make it a paste.  Let it sit on there a while, then scrub with a scouring pad.