* Via Bluetooth from your phone. Model 3 and Y used this as the primary way of unlocking. This does not require a Tesla server. It's just local communication between the car and the phone. The car and the phone are paired.
* Via a key card. Model 3 and Y use this as the method when you get the car until you pair it with the phone and what you use if you want to give someone temporary access to the car (e.g service, valets).
* Via a key fob. Model S and X used this in the past (not sure if the latest refresh changed this but older S and X vehicles didn't support Bluetooth or Key cards) as the primary method.
* Remotely via the phone app. As in you make an API call to Tesla with your Tesla credentials and Tesla sends a remote command to the car. This requires Internet access for the device making the request and to the car in order to receive the command. This last bit is what's broken. Given the requirements this has never been very reliable and nobody would want to use this on a day to day basis.
So I seriously doubt very many people are locked out of their cars. I am able to get into my 2015 Model S via the key fob and my 2018 Model 3 via Bluetooth from my phone.
For what it's worth I also didn't mention that at least the old fobs also had an RFID in them that if the battery was dead you could just hold them up to certain spots on the car to open/drive it.
My phone battery lasts all day, and the internet is rarely down; but servers on the other hand...
An app is a great backup to have.
So, you carry the keycard in your wallet in case your phone dies or it is stolen or whatever, you can still get in and start your car. But 99.999% of times you just walk up to your car and start driving without unlocking, or turning a key, or anything like that.