This may be colored by my experience of mental illness, but generally I've learned/grown more from pondering and sorting out feelings in the past rather than right now. It's easy to fall into a trap of "worshipping your pain" (or your hypomanic euphoria for that matter).
OTOH I'm very appreciative of the dispassionate attitude encouraged by stoicism and meditation, etc. -- but that kind of wisdom is acquired with work, like building muscle. "You should lift heavy things!" is both an interesting aspirational model and dangerous advice if it isn't culturally obvious that you can get hurt lifting heavy things while not in shape.
(Edit: stoicism/meditation etc. are more or less like "second-order repression": as you acknowledge your fingertips or your breath, you acknowledge that you have feelings in order to theoretically understand them (locus of control/illusion of self). The danger is that letting go of first-order repression, you can let yourself have feelings about your feelings -- feeling good about feeling miserable would be the common type.)
I like to think of my self as happy Sisyphus enjoying pushing the rock up the hill. Thinking about the futility of the effort is by definition futile.
Try as I might, I have no idea what this has to do with feelings. Are you making an assumption that people who acknowledge or express their feelings are not handling problems?
And of course, as others have pointed out, stoicism doesn't suggest not pondering over feelings.