So you're firmly cleated in, on a new route and suddenly you hit a hill. You click up a gear, hill still steep, hit a bend and steeper. Realize you've got a bit of a problem....
I would have already known was coming. I plot my new routes using OS maps and I look out for the chevron symbols. A single chevron is ok (14-20%) - I know that I can handle
those hills. Double chevrons... Houston, we
might have a problem (20+%)! I would have a look on Streetview and also search online to see if anybody had described riding up that hill.
Out of gears and you this thing is still getting way steeper. You can't keep up and know you need to bail. Fast.
I took the precaution of putting a triple chainset and big cassette on my bike so I have a much better chance of getting up those nasty steep ramps!
What do you do? Hit the brakes and accept you're going to topple over? Probably crushing yourself and your carbon frame in the process.
If you are on such a steep ramp that you are about to fall off, no braking required - you will come to a halt in less than 1 second and you need all of that time to get your foot unclipped so leave the brakes alone!
Or do you try and pull a quick turn back down the hill so you can control yourself off the bike?
Don't even think about attempting that turn - if the hill is as steep as you say, you would likely fall off!
Oh wait, there's a car behind you...
Funnily enough, I just found a diary from when I got back into cycling in 1989. I found a report of riding up a monster local climb but failing 3/4 of the way up. I can clearly remember it happening - I had managed the 10% bits. I had got up the 15%. I survived the 20% and had suffered like hell up the 25% and I thought that I was going to get round the LH bend after which the gradient settles back down to a manageable level. An idiot driver had other plans for me...
Got up this...
But the driver overtook me on this evil bend, which is about 35% on the inside, forcing me onto the cobbled bit...
My legs seized up and I fell to my left, fortunately landing on the grassy bank. I had toeclips and straps on that bike so it was impossible for me to dismount in a hurry. I saw the error of my ways and replaced the pedals...
Unfortunately, I replaced them with Look Deltas (as you can see in the photos above). They were the model before the Keos, but the same idea - a big piece of slippery plastic attached to the soles of your shoes. Not good for emergency dismounts! In the photo above with my bike halfway up the 25% ramp, I had actually just done an emergency dismount, fearing that I was not going to make it round that bend. Guess what? Yes, the Delta cleat slipped from under me and I nearly faceplanted on the road!
So... the Deltas had to go too! Now, all of my bikes have mountain bike-type SPD pedals on. The aggressive tread and recessed cleats on SPD shoes are ideal for panic dismounts.
I must be missing something as unclipping takes a second or two, no more which has always been ample time to get my feet on the floor before I topple over.
You are missing riding up 20-30% ramps!
Put it this way, if you are fit enough to ride up climbs that steep fast enough to be able to coast for 1-2 seconds then you probably would not be having to dismount...
It won't happen. No road in the UK no matter how insignificant, is steeper than what a loaded packhorse could manage so a cyclist can get up it even with a bit of a sweat.
Pardon me, but, er -
billhooks!

Here is a Pennine packhorse trail with 2 cyclists on it...
I'm sure that there are
some cyclists who could get up that climb on their bikes, but I didn't make it and those 2 didn't either - we were all pretty fit at the time. I'd guess that 90% of riders would walk the steepest part of it.