Yes, glacier ice purer than regular ice, and it is not surprising that some entrepreneurs have marketed it commercially for drinks.
There are several scientific and aesthetic reasons for the superiority of glacier ice.
First, the ice in glaciers is relatively pure water because after thousands of years of compression of the tiny snow grains laid down in ancient times, all the impurities have moved to the boundaries of the grains and been flushed out.
The final ice, especially if it comes from a single crystal, is much purer than the original precipitation, almost like triple-distilled water.
From an esthetic point of view, a glacier has crystals in it as large as or larger than refrigerator ice cubes.
In a single crystal, all the molecules are lined up, while a regular ice cube is many long thin crystals. As a result, light refracted through a cube of glacier ice is much more beautiful than the cloudy light play of refrigerator ice.
There may also be sound effects with glacier ice.
When the snow was deposited in the pack, a lot of air was buried with it, and over time, the air is compressed into little bubbles surrounded by ice.
A thousand meters deep, the air is under fairly high pressure, but when the bubbles are freed by melting, the air pops out with a pleasing crackle, creating a sparkling drink without adding carbon dioxide.