Chromatic aberrations cannot be removed using a material of just one refractive index. And as the video shows this lens has chromatic aberrations.

Some of the blurriness seems related to melting on the surface layer. I wonder if he had made a metallic lens housing which was supercooled to prevent melting if the result would have been better.

Using distilled water doesn't make ice much clearer. There will always be impurities (like air) in the water which get pushed towards the center of the ice as it freezes. Another issue is that ice is less dense than water, so in a partially frozen ice cube the center will require more space when frozen than is currently available, leading to cracks.

To get clear ice, you need to freeze water directionally, in layers. It's the only way to get clear ice.

I make clear ice at home with those specialized insulated/rubberized coolers. The distilled part I mentioned is in relation to impurities and that glacial ice was the most “pure”. Is that really true? Can’t glacial ice have trapped impurities and gasses?

I guess what I’m getting at is, the claim that glacial ice was needed, what particular property of glacial ice can’t be replicated by careful ice making?

Glacial ice is just compacted snow so you're going to have some amount of other crap in it (hence why we use ice cores to learn about the atmosphere at the time of their formation). Glacial ice that includes whatever year some big volcano went bang is probably not going to make a very good lens.

I suspect that lab ice made with the express intention of being clean would be far cleaner.

The glacial ice is pure artistry, not something well though out. This is shown by the fact he didn't consider his iceball maker wouldn't work as fast in cold conditions.