Spyderturbo007, It looks like the nut is still on the broken screw in your first photo. If you don't remove the nut from the back side before turning the shoulder screw, you'll break it every time.

Yep, This is the reason why I rarely take them apart anymore. I have freed some up that seemed like they were welded on without removing that screw. I use synthetic Super Lube to soften and get it moving. Followed by a solvent like 91% alcohol or mineral spirits. I liberally flow the solvent on and scrub it with a toothbrush until all the old grease breaks down and is removed and it pivots easily. Then I add one drop of super lube where they originally put that grease. I did some like this over 20 years ago (some with and some without the extra drop of oil) and they all still move freely.

Other sticky pivots that just require removal of a pin or clip I still disassemble to clean, but these just aren't worth the risk. If I couldn't free them up I would still take them apart, but I haven't found that necessary, so far.