It very much does warn you to take over, i'm not sure the SAE levels specify how much time the L3 car should give you, nor do i see any specific reliability requirement. The wheel nag and "attention" camera are the only things stopping it from being outright L3 and even that is debatable.
Really tho, IMHO, there is no up side for Tesla going after the L3 tag right now. All it would do is create needless hurdles for them. Most consumers aren't even aware of the "levels" and even if they were, people are focused on what the thing can do (in this context) rather than what its called. And considering tesla pretty much has 0 competition beyond marketing BS from other companies (i mean look at the production and sales numbers of EV's from anyone, let alone what other car makers call ADAS, its laughable). Plus given the fact they, clearly, have no need for marketing anything atm, it would be utterly pointless for them to pursue that and would only take resources away from more important tasks.