In reply to im off:
For straighforward ice climbing, climbing is ski boots is not too bad. The added support is beneficial for reducing the strain on your calves when doing front pointing. I've done a number of moderate alpine ice routes while wearing ski boots.
However, skiing in mountaineering boots is very bad. Any significant downhill is going to be quite difficult and you will likely end up wrecking multiple times (unless you are a highly skilled skier.) Also, touring bindings are not designed to work with softer mountain boots. The release mechanism is made for a ski boot, and a soft boot won't transfer the forces to the binding's release mechanism effectively, so you're much more likely to break bones in a crash.
The only situation where a Silvretta and mountain boots are the right option is if you are traversing relatively gentle slopes with no significant downhill skiing.
If you're looking do do a moderate ice route on the Triangle, and then ski down the Valle Blanche, the answer is to both ski and climb in modern touring ski boots. If you are climbing something that requires both difficult skiing and difficult climbing, then bring both mountain boots and ski boots.
The Arcteryx Procline was an attempt to make a boot that could both climb and ski. It wasn't great at either, but was not a bad compromise. However, it's long since discontinued. Some of the lighter and more flexible ski boots (like the Fischer Traverse series) make pretty good climbing boots, so long as you don't need to do any flat foot French technique.