The issue is where there hell am I gonna find a monitor everywhere I go? Continuum only works IF you have a monitor (not only one that is actually present but also able to be plugged into a power source) keyboard and mouse.
Why it doesn't work is that you cannot guarantee that you'll be able to have all these peripheral available everywhere you go. You mentioned it possible to have this setup at work - I will pay that to some extent but Office mobile is woeful and that's also only if you use Office. Photoshop? AutoCAD? 3dsMax? Illustrator? Forget it, won't run on your phones.
Hotels? Yeah maybe but now you'll probably have to supply your own cables as well, (phone, dock, cables, keyboard and mouse as they won't supply those) Your bag is starting to fill up.
I feel that Continuum answers a question nobody asked and to be honest answered decades ago - Laptops. They work, and they work well. and laptop guarantees and screen, keyboard, touchpad and most importantly a battery, so no need to be plugged into anything for power. And in todays engineering marvels, laptops are now ridiculously thin and light (copyright Apple) ain't so hard lugging it around.
Cafe's and restaurants? No way. I know I'll get some grief for this but if you ever go to Starbucks you'll probably be undated with a sea of MacBook. Some are just for show but some are actually getting stuff done on them, and the best part for the Cafe's are they don't have to do anything. The person with the MacBooks comes in to fairly empty table, place MacBook on table, starts work. When finished, closes Macbook, leaves tables fairly empty again as he found it.
Contrasting this with a Continuum scenario:
Comes in and sits at table. Now as a Cafe I'm fairly certain there won't be any monitors at the table - it'll ruin the mood. So he what? Walks up to the front counter and asks
"Do you have any spare monitors and keyboard and mice? I need to get some work done"
At this point the person behind the counter laughs at him (who asks that sort of question in the Cafe? Nerd) or in the Microsoft daydreams,
"Yeah we have all that stuff in the back spare room. Funnily we thought about filling that spare room with extra food or turning it into a small chill room for the staff but then decided it's much better to fill it with monitors and keyboards and mice! Staff love it"
They then go to the back room rummaging until they find all the gear and then awkward carry it all back to the Continuum guest, apologising as they smack the heads of the other customers with the corners of the gear.
"Umm sorry sir you can't sit here as theres no place to plug the monitor into, you'll have to find a booth seat"
"But there are no empty spots? They are all filled?"
"So it seems..."
Awkward silence
I can see happening in a lot of places, you'll be forever asking "Do you have...?"
Someone with a laptop doesn't need to ask