Exceeding 10,000 ft. is orthogonal to needing anti-/de-ice systems. In fact, you're often less likely to need them at the higher altitudes because it is too cold for airframe icing to occur. Counterintuitively, if it is too cold, you no longer have icing problems.

You need to pass all of the feet leading up to 10'000 feet though.

You can use the batteries as structure and they produce heat that you need to cool anyway. Seems like there is a lot you can do with that once you start optimizing everything around the battery.

I don't know how much weight a anti-ice/de-ice could add.

My point was only that once you think about it and redesign everything around the new constraints, you can come up with things that we don't yet think about.