The valley station is right across the road from the SBB station building in Unterterzen, if you use the "right" carriage (expect it to be packed tight) the asphalt shouldn't be an issue at all. It wouldn't surprise me if they even used rubber "carpets" nowadays as that also reduces the risk when people stumble and fall.
The people at the SBB station won't mind you calling (preferably off peak) about the availability of lockers and other stuff.
Have not done it but here is what I would do. If you have a ski boot bag/backpack, I would use that and take all your gear in it (helmet, gloves, boots, snack etc). Then you can either leave it at Flumserberg Bahnhof or at Tannenboden (the arrival of the gondola which take you from the Bahnhof to the slopes).
They have lockers there but if all taken, a ski rack in fron of one of the restaurants will do also. No one will steal that stuff.
Yeah, I have seen tons and I even did it myself in the past before I realised its far more convenient and comfortable to take a ski and boot bag and then just get a locker when you get there. However, now I always go by car and my ski life is far easier and more comfortable.
I struggle to believe that you have never seen people wearing boots on the train, it is a fairly common sight, especially for ski tourers that have to minimize stuff they take. Also a lot of people still don't think about getting lockers.
That's what I thought too, I'd even say my impression was it's the norm, if your boots fit well enough it's no big deal, just wear them loose and tighten for the slopes. And you get to make robocop noises to yourself walking around the HB.
You'll need new boots long before you suffer any significant wear on the sole.
I normally take a picnic lunch to eat on the slopeside, and so take a small backpack with me (also containing a water bottle, sunscreen, and a few snacks, plus a book for the train). I travel wearing lightweight shoes and carry the ski boots with the velcro bands attached to each other to make carrying them easier. I don't mind travelling to the slopes wearing ski boots, but that the end of the day with sore legs and feet it is really nice to be able to walk in something lightweight and comfortable. This way there is also no stress about trying to find a locker.
I used to go to Flumserberg on the train lots and always left gear at the lift station lockers. No issues. If you are not sure, just ring them and ask. The mountain resort people are 95% of the time very friendly and helpful.
I used to wear trainers and put them in a backpack, but then I got fed up of having a backpack with me and just wore the boots on the train and saved all the hassle of dealing with backpacks or lockers.
Wearing the boots from home is ok, I have done it one or two times.
but I would not do it if you have to walk a long distance to the train public transport.
What I do currentl is to wear sneakers that are small enough to store in my day backpack. (bring a bag or something to isolete them from your food ;-) ). Then I carry my boots on the shoulder tight together via the velcro strap.
I took a lightweight backpack & wore a lightweight pair of trainers on the train.
I was able to fold up my ski bag, boot bag and put that and the trainers in the backpack. It was pretty lightweight so I just skied with it during the day and changed at the end.
There was even room for some sandwiches on the train back