The incompetence of the turnstiles makes it a good focus for the story while the juxtaposition of the turnstiles with Jira exposes the company's hypocrisy.
It's an issue but I wouldn't call it a particularly big issue. I don't think it's very damning for how much the company cares about security.
And it sounds like the turnstiles did work for actual security? Sure, they gave up on per-floor security, but that's a lot less important.
Edit: And if employees are reusing passwords then we should be getting them password managers (or SSO) as the top priority, much more than we worry about logins in cookies inside the building. I mean, there's a point where a single purpose password and a login token become the same thing.