Where I work dev team also does the L3 support: we have L1 who can change the password, reboot the computer, we have L2, who know the basics of our app and its surroundings, but if an issue is not obvious to them - here we come!
Also, the "real purpose" of L1 tech is to categorize and prioritize incoming calls for further L2 / L3 processing. Knowing "who" needs to handle the call next, and its priority, is usually critical to getting real problems resolved timely.