Over the years I've done a fair amount of reworking documents from "he or she" style to "they" style.

I've found that using "they" style does quite often make it harder to be clear, when you've got a sentence that's talking about both a person and some things.

Something like

"Then the operator must update all the rules. They must ensure that no bad things happen."

Does the "they" refer to the operator or the rules?

Of course you can always rephrase to make it clear again, but you're losing a certain amount of freedom of arrangement that you might have wanted to use for other purposes.

As a matter of language use only, the phrase "They are coming over to my house later". Should I expect one person, or multiple people? Should I go out and grab a 6-pack of beer for my visitor(s) or a case? Easily clarified, and I'm happy to use people's preferred pronouns, but let's not pretend there isn't the loss of precision there.

It is very convienent. It gets unclear when people try to substitute it 1-1 for he or she in situations when the number of people is unknown.

I use they as often as possible, but the writer needs to build their sentences with it in mind.