You seem to have ignored the important distinction - there is no government approval needed.

Even if you have outstanding debts, you can still dissolve the LLC. Of course creditors can cause trouble for doing that, but there is no government approval in the process.

In every state in the US I'm aware of, you must file for a certificate of dissolution with the state department. You can't do so unless you're in "good standing". In effect, you're not allowed to complete the dissolution until the state permits it.