First off, if it works for you and you are happy then just ignore me but I just thought it would be worth giving a bit more of an explanation and apologies in advance if this is obvious to you:
Moving the balance all the way to the right effectively discards the left channel completely.
Left and right audio channels will carry different audio information, how different depends on the source:
In a film if two people are talking on either side of the screen then it’s common for the majority of their dialogue to come from their own side, left or right. This means that in this situation you will not hear the majority of what one character says. I don’t watch much TV drama so I can’t say how much of an issue it is in dialogue outside of films. Also in films the stereo channels are used for sound effects: a distant train will get louder in one channel as it approaches and then louder in the other as it leaves.
In music, as @z10user2 wrote, it can happen quite often too, one instrument will be stronger on a particular channel, or the levels can change as sounds move from one sie to the other.
For news, documentaries and other types of content, differing stereo channels are rarely used for any purpose so you probably won’t notice a difference.
If you don’t watch many films with special effects or listen to music you probably aren’t missing out on much but if you want a belt and braces approach then I’d do something about mixing the channels together so that you aren’t loosing any sounds from your listening experience.
I did originally think that maybe you could put the offending hearing aid into flight mode which means that it wouldn’t receive any transmissions but I’m not sure that would work.
Final thoughts: I had a similar issue with my right ear and streaming but I’m a DIYer and fiddled with the fitting, specifically I performed an uncomfortable hearing test which to my surprise uncovered a sensitivity that I have at around 3kHz. Once I added that to the fitting, listening was comfortable again.