I have Continental TS 870 PS winter tyres and have run a set of winters tyres (and wheels) in the UK since about 2014. Over which time I've had Continental TS 830P and then 860 on 17" wheels. Now the latest iteration 870 PS on 18" wheels.
Granted I've seen the wheel swop date due to the magical 7°C getting later and later. Used to be late October, but in the last few years it's been very late November. I usually make the decision to swop when my early morning commute is consistently below 7°C for about a week or so.
Driving about 30k miles a year my daily commute in the winter months sees me leaving home about 7 am and leaving work at 5.30 pm. During which the UK temperatures on my commute would generally be 4 to 5°C (or a few degrees less in the mornings) as I went up and down the Midlands, much of it cross country on B-roads.
Granted if you decide to drive like a loon round corners you can feel the tyres squirm (technical term

) compared to summers, but then that's to be expected. But I don't and I'd rather have the overall grip reassurance in cold and wet or frosty/icy conditions. In wet weather conditions I've not had any issue with them in terms of braking. In my opinion I also find they're better when the road is greasy compared to summers. I would echo GolfDB's comment but in a winter tyre usage, when the temperature drops you can tell the difference.
My Continental 860s were due for renewal this year after 4 winters' use. I did think about whether to go with all-season tyres this time around, as I know they've come on a long way in terms of performance. I watched a few videos and reviews. However in my case I decided to stick with winters. That may change in the future if the UK continues to get milder winters and I don't drive when it's generally still pitch black for my morning commute.
I think you have to make the decision based on researching the tyres, but also what's right for your driving. When you drive in the day, what types of roads you drive, the distances you drive and where you are in the UK.
The Michelin CrossClimate 2 does look to do really well in testing and reviews. I've not driven on all-season tyres so can't comment on them. But I think that whichever you pick, all-season tyres or winters, point is they'll perform better than an equivalent summer tyre if the mercury remains under the 7°C.
Winter wheel wise I have the 18" BBS SR Himalaya Grey. All the reasons you've stated, a simple design and easy to clean, importantly they're not diamond cut which can take offence at gritted roads

. I wanted something durable and not easy to crumple in the face of nasty unexpected pothole.