No-one has yet addressed the question of why a respectful term for males, and a respectful term for females, should be two different words.
Probably because no one thinks that?
What we object to is the 'neutral' word being the male term (yet again), not the concept of a catch-all.
If we can name a thousand and one genders we're certainly able to come up with a truly neutral term. We're a creative species like that.
Companies have no gender
In reality, you're addressing the directors of the company. The expectation is that they're male. It's not a coincidence that it's 'Sirs' and not 'Dear Legal Entity'.
I think says something about the legal profession
To be fair, it's not all of us! My (large, international) firm has banned it. Some partners do cling to the old ways and some letters will slip through, but it has been recognised as outdated and not how we wish to do business. Thankfully, I'm seeing it less from other bigger firms now too. I do think it will die out.
Can you give me an example of this oft occurring phenomenon?
A person's sex is male. They identify as a woman. Their 'gender' dictates they are to be addressed as madam rather than sir. Otherwise, the speaker runs the risk of being accused of a hate crime which could result in the the full force of the Twitterati being brought down upon their head and a complaint being made to West Yorkshire Police so their thinking can be checked.