I’m pretty sure GP is saying if you already had an account and you delete it, it’s trivially easy for someone to register with your old handle and impersonate you
Of course people can always impersonate you but the goal here is to prevent them from impersonating you with a social handle people knew you had.
If I recall correctly, the handle you deleted stays inactive and is unavailable to new registrants. This is present on Google at least, I assume it's the same elsewhere.
The concept of a handle goes beyond a username. If someone can construct a profile that looks like someone's profile on another site and contains approximately the words in the username, like _username or imusername instead of username, they might be able to impersonate it. In that case it would be good to have an active profile on that platform to counteract it.
That's an interesting point that I had not considered. In that case, your handle itself is the unique identifier. That said, if I recall correctly some sites do not recycle handles, but this is still an interesting point nonetheless.
Of course people can always impersonate you but the goal here is to prevent them from impersonating you with a social handle people knew you had.