While it's true that the singular they/them has been used for a very long time, it was used in a very narrow context. It was used almost exclusively for an unknown person, or a theoretical person. In your example, the suspect is unknown, if it was known that it was a male suspect or a female suspect, the suspect would no longer be as unknown and so the sentence would probably be changed to "The suspect entered the store, then she exited through the back."

You can tell that it had a very restricted use because of how "themselves" was used. For example, "anybody who wants one can get themselves a beer". That's a singular construction, but in a way that it might apply to multiple people individually. There was no need for "themself" because "they" was always used for unknown or theoretical people.

Using it for a known person, especially a person who might be currently sitting in the room, is a brand new and confusing use. Now, it's not like English doesn't have other confusions, even around pronouns. Take: "she was drunk and her mother was angry, and she slapped her". Who slapped whom? Sometimes the pronouns alone aren't enough and you need to restructure the sentence to make it more clear. But, the fact that the singular they is used with the same verb forms as the plural they can add extra confusion. Take a non-binary player playing a team sport: "They're not playing well but they are." If the personal pronoun version used "is" instead of "are" it would be less confusing in situations like this, but it would be more confusing in other ways because "they" could use both plural and singular verb forms.

It would be just as confusing if people suddenly started using "one" as a pronoun not used for a theoretical person, but for a concrete and actual person. One has been used as a subject pronoun: "One must remain vigilant", and an object pronoun: "Wounds can make one weary." But, it is always a theoretical construction, it has never been used to refer to a specific, known person. So, it would be confusing to start using it that way: "Give it to one, one doesn't have one yet." But, even that would be less confusing than singular "they", because at least "one" uses singular verb forms, etc.

They/them for a specific, known individual is a new way of using "singular they" and it adds a lot of confusion You can argue that despite the confusion it's necessary, but you can't pretend that it doesn't add confusion.