I am starting to wonder where the 273,000 (so far) Model 3 owners are going to be charging their new cars when they finally get them. I keep thinking that at some point, when electric vehicles become more and more popular, finding a free charging outlet when you need it is going to take some luck.
They will probably charge at home like everyone does now. Sure, public charging will be a little more in demand, but with 215 miles of range available every morning, it won't be necessary.
Even now when people find Teslas plugged in to public chargers there is usually some ire since they don't need it as much as a LEAF.
I doubt Tesla owners in general will use public L2 charging very much, unless it's free, and maybe even then. Charging at a 30A EVSE at the US average of $0.12/kWh saves you about $0.80 per hour charging on your power bill. I don't think many people would drive somewhere and wait to save a few cents.
L2 is simply not needed most of the time for daily driving - if you're plugging in at night then it's easier to plug in once per day rather than twice per day. This is actually true even for lower-range EVs as well, which is why public L2 infrastructure is vastly underutilized on the whole.
However, Richard230 has a very valid point for Supercharger congestion. Tesla has a more complete picture, but their most recent public numbers show ~20% of miles being charged on the Supercharger. I expect this to increase slightly for smaller capacity EVs like the Model 3, and as Tesla expands the Supercharger network and more types of trips become possible. Unlike L2 charging, charging on the Supercharger is a significant cost savings (~$15/hour), which will factor into some charging decisions as well - people may stay longer than needed simply to reach their destination.
Tesla is pricing in Supercharger expansion, maintenance, and operation into the price of their cars; presumably this will allow them to scale the Supercharger network as demand ramps up. Very much worth noting that this will require linear scaling of only the significantly utilized stations (maybe 10-20% of the network today); a large part of the network exists to allow occasional longer distance travel over less frequently traveled legs, as opposed to short trips that occur on very heavily traveled legs.
Tesla has all the data to enable them to scale this up and I trust they will be good stewards of the Supercharger network, certainly better than Blink / Chargepoint; it is one of their crown jewels, and by pricing the cost of the network into the upfront price of the vehicle they have the financial resources to do so.