So, if one was arriving at T4 and planning on a taking a cab or an uber to leave LAX, could the quickest way now be to go to the arrivals level, grab the very first hotel shuttle that comes along, then either arrange an uber from that hotel, or grab a taxi from there? You'd avoid LAXit, and airport fees...
The LAXit bus would take you nonstop to where you can walk 2 minutes to Sepulveda and Century. From there you can summon Uber or take a city bus. This should be slightly faster than your method.