Currently if you search for an artist which has a non-latin name, you will get:

• artist name in native script
• artist name in your locale (in my case latin)
• artist sortname
• artist disambiguation.

So for Tchaikovsky you get:
"Пётр Ильич Чайковский, Pyotr Ilyich Tchaikovsky, Tchaikovsky, Pyotr Ilyich, Russian romantic composer Pyotr Ilyich Tchaikovsky"

Obviously this is ridiculously long and redundant, but also the commas in the sortname really confuse things — it's hard to tell where the sortname begins and ends. It also doesn't help that this particular case includes the artist's Latin-script name again in the disambiguation.

IMO we should at minimum treat the sortname as a fallback (only display it if there is no native-locale artist name).

In order to encourage adding native-locale aliases, I would also be fine if we never displayed the sortname at all and let aliases do the job entirely.