tube DAC noise

I have no experience with the Black Ice to know if the noise is inherent, or simply that you have noisy tubes. Try swapping in some tubes that are rated low in microphonics

To your question if all tube DACs are noisy - I have a Modwright Elyse tube DAC and have zero noise issues

I own the Jolida version of your Black Ice DAC, and I have had no noise issues with it.
Originally, I did swap out the stock tubes with replacements . That, may have prevented me from experiencing the same problem as you have.
I own a tube preamp, and, after two years, it developed a hissing noise. I swapped out the stock tubes with new tubes, and that took care of the noise.

My experience is that tubes have noise.  Usually not circuit topology.

No, tubes are not noisy. I have all tube equipment on my main system and four headphone amps..; no noise... none. Total of nine components.
One can get a noisy tube occasionally. Sorry don’t know anything about black ice. 

My jolida fx dac had hum issues no matter what interconnects I used. It was someplace in the rca jacks...checked them and they looked ok...I promptly sold it. Waiting for my border patrol to arrive. 

If using NOS tubes, always have them tested for noise and microphonics. Upscale and Andy at Vintage Tube noise test every tube sold. Brent Jessee charges $10.

There's no noise or tube hiss from my Audio Note DAC.

No noise from my MHDT Lab Pagoda using the stock tube or its replacement.

There's a reason (OK, more than one) why Jolida / Black Ice stuff is so cheap.  Build quality on some of their products leaves something to be desired.  No tube noise from my MHDT Labs Orchid.

...thanks greatly for the experience y'all.  I tried different tubes, all from upscale, and was never able to rid the unit of noise so I sold it off.  Recently been considering a couple different dacs and some are tube based and have naturally been hesitant to try.  Will have to keep experimenting with an open mind.....

Border Patrol uses one tube as a rectifier. No tubes in the output stage. Good reviews and owned by quite a few members.

nope - need good quiet tubes

I have the Doge tube DAC and it’s dead silent, and it uses 8 tubes.