I absolutely add a couple coats of wipe on polyurethane on any cabinets I paint. Yellowing polyurethane is mostly confined to oil based polys and cheap water based poly. But there are many different higher quality water based polyurethanes that will dry absolutely clear and remain that way. Without poly, especially on high traffic cabinets, things get dingy and cleaning them all the time wears out the paint which is what you are seeing. Another newer option is polycrylic which has a lot less VOC's, much safer to work with (not flammable) and dries faster. But it is thinner than polyurethane and harder to apply on non-flat surfaces without getting lots of runs and drips. Also, if you apply it too thick, it can get a milky appearance which might not be an issue with white cabinets but is definitely an issue when applying over stained wood. For polyurethane, I usually go with the Minwax water based wipe on poly. I have also heard but never used General Finishes wipe on water based polyurethane is pretty good too. Minwax also makes polycrylic too.
As for the bannister, unless it is a very simply shape, i.e. round with no inside corner features, I wouldn't bother stripping. Stripping outside corners or rounded features is pretty easy. Stripping concave features or inside corners is extremely time consuming, much more time consuming that stripping is in general. It also depends on what kind of wood is underneath it. If it is open pored, you can strip all you want but until you remove wood down below the depth of all those open pores, you are going to see spots of white paint forever. If you want to leave the bannister railing painted, I would clean it well with a degreaser and soap and water and then prime and repaint it. As for a top coat, poly is a good choice especially if you want to clean it often to remove grunge. On my bannister, I apply a paste wax to it about once a year. The paste wax doesn't harden so it has a softer feel that I find more pleasing on objects I touch frequently and it has a softer look when viewed in the light. But paste wax is a wearing finish so it needs to be reapplied from time to time.