I don't fly a de-iced plane but I don't think there is a connection between single-engine and icing conditions capability. A SE can be just as capable as a ME.
The difference is in systems redundancy, but even there the situation is clouded. For example a G-reg TB20 with full TKS is OK for icing but an N-reg TB20 with full TKS isn't, largely because the FAA require two alternators. But the backup alternator is nothing to do with icing capability. I am reliably advised that a TB20 with full TKS is exceedingly capable in icing conditions.
But nobody wants to spend a 4hr enroute sector in IMC collecting ice, which is where an additional operating ceiling comes in, and a turbocharged plane with a 25k ceiling will have a greater mission capability against icing conditions than a non-turbo one with say a 18k-20k ceiling. This is because typical stratus cloud tops are rarely above 16k so one needs to climb above it and then you (usually) have sunshine. If the tops are a lot higher than this, it is due to foul weather (e.g. frontal stuff) or lift up a mountain, and a decisively higher ceiling is required.
With a 20k ceiling, I estimate a 75% random-date despatch rate if not de-iced, and perhaps a 95% despatch rate if de-iced. To get beyond that, you need the capability to handle frontal weather not just enroute but also in the end bits, which needs more kit: radar and a higher ceiling, or (for the brave) just radar
And the cost starts to rocket up.
Personally I am happy with my 75% rate, achieved with a TB20 with a TKS prop. If I wanted a decisive increment it would have to be a Jetprop - a Malibu Mirage with a proper motor up front. The piston Mirage has had (according to one report I've come across) a 10% in-flight engine failure rate which is a complete joke.