Answer: it depends. Your bike may not have the same gearing mine does. Your *body* may not have the same function (or lack) that mine does . I do try to avoid going straight from 2/1 to 1/1 on my bike, because it just doesn't work well.

I keep doing hard things (like hill climbs) where I'm not quite sure what the right gearing solution is. So each attempt, I try a new technique, or I try for better execution of something that sort of worked the last time. Some of the improvement I see in my hill climbing ability is just plain old physical strength. Another big chunk is I make better use of my gears. If I end up having to walk, it's ok. I won't learn anything if I don't try.

On my nemesis hill (a piddly 5% grade *sigh*), I've tried all kinds of techniques. Since I have a short downhill right before I go up, what seems to work best is to upshift on the 2nd chainring for the downhill, maintain speed on the little bit of flat, and drop into the 1st chainring as pedaling gets hard. So I might go from 2/5 to 2/6 on the downhill, drop into 1/6 as I *just* start to stomp on the pedals. That leaves me with 6 gears worth of downshifting for the hill... still not enough but I keep doing better. On my first try, I barely got past the first of 3 cross streets on the actual hill. On my most recent try, I got up to the second cross street, and stopped the bike a little early because the curb was a safer dismount.

Each hill is different. Sometimes I can upshift while going up a hill, because the grade is so shallow. Other days, the same hill is a depressing downshift party.