I like my clipless pedals. I am more comfortable using them for longer rides. I think I fell over once from forgetting to clip out, and that's all it took. I use road pedals on all my bikes but 2 (one mountain bike and my beater mtb). If I have to take a trip while I work, I just ride on the top of the pedals. It's comfortable enough for a few miles. I don't tend stop for stuff on the way home, though I have been thinking of getting one of hte shimano platform/clipless combos anyway.
As for bringing shoes to work...I do that. I have an old pair I leave here in the case I forget to pack a pair, or am loaded with other stuff. I don't like wearing shoes I have been sweating in, so I would do it even if I didn't have to change out of my bike shoes.
Cages don't work for me. I recently sold a bike that had them. They scuffed up my shoes, and having size 13s meant my feet didn't always have enough space on the pedal.
My one bike I still have platforms on (beater mtb) gets ridden usually for trips under 5 miles. I find myself still going through the motion of unclipping subconsciously. I don't see much reason to put clipless pedals on that bike due to the short nature of the trips I use it for...but I do tend to feel less "in control."
As for stopping and such...it is only a twist of the ankle, and I come out of my pedal long before I have actually stopped. The only times I have had problems is mountain biking on an especially muddy day...the mud gunks things up. Just have to remember to bang my feet before I clip in. I had some issues with it being hard to get out quick, but a few squirts of GT85 later and all was good n easy again.