If the city is getting uppity about a permit for a 14-50, then get a NEMA 6-20 and buy a TurboCord. It'll be cheaper than upgrading your service, that's for sure.
Some of the Teslas will slurp up 80 amps, which is a lot and I am not surprised electricians see some shenanigans. I only have 100 amps at home, and we have two EVs too, plus and electric stove and an air conditioner. Be that as it may, we never really crack 50 amps whole house, and usually not even above 36 amps except for a few seconds here and there. We've never popped the main. Not even close.
We run the chargers at 12 and 16 amps and charge late at night or first thing in the morning when nothing else is on, plus some other tricks in the setup.
Definitely consider a charger that you can change the power on, and set it to the lowest you can live with. Every component in the system from the panel to the charge port in the car will thank you for the lower heat load. Even when everything "works fine" there's no real point in running any hotter than you actually need to.***
If you're a real nerd, you can set the charger up to drop back to 6 amps, or even sleep when the air conditioner or stove turns on. (Home Assistant, MQTT, OpenEVSE, OpenEnergyMonitor)
*** There are arguments made about whether lower or higher amperage home charging is more efficient, but the differences, if they exist at all, are hard to spot and too subtle for most grownups to worry about.