Triplefault gives an excellent overview. +1 - check your local NEC adoption, plus local amendments, and don't forget the load calculation.
But you are probably wondering why does it really matter? I'll give an example: hair dryers. For decades, portable consumer hair dryers have had a GFCI built in to the cord/plug. Why? Because at the time GFCIs had been proven lifesavers and most homes did not have GFCI-protected receptacles (whether protected at the breaker or the receptacle is irrelevant, they just weren't protected at all). Even today, many older homes still do not have GFCI-protected receptacles because in most cases adding a GFCI is not required if the circuit/receptacle was installed prior to 1975, and even later for states that delayed adopting the 1975 NEC.
If you have a hair dryer with a built in GFCI and the hair dryer drops in the sink, the GFCI will trip and save you from injury or death. However, if the receptacle itself gets wet and the hair dryer is not plugged in 100% and the cord gets wet and your hands are wet and your feet are wet then you could still get zapped, unless the receptacle itself is protected. Is that common? Hopefully not, but it is not nearly impossible in a bathroom. Adding an extra $5 (probably less by now) to the cost of a hair dryer isn't so bad - people will accept that. Having to suddenly hire an electrician to add $20 GFCI/receptacles - and add in labor costs far more than that - people just won't accept that. They'll do it when they remodel the bathroom or are having other electrical work done, etc. The end result is that some people just don't have that last piece of protection, but that is the nature of safety rules and cost/benefit analysis.
So back to your EVSE. Plugging in your internally GFCI protected EVSE in a non-GFCI protected receptacle protects against you getting hurt if the cable is wet and the car is wet and you are wet (let's say it is the middle of a rainstorm but you have to drive somewhere). But if the receptacle is also wet, and the plug is not quite 100% in (these 50A 240V plugs are big and heavy and hard to plug compared to 15A 120V plugs) then you could still have a problem. GFCI-protected receptacle (which necessarily means GFCI/breaker in this case) solves that problem.
Why doesn't a hardwired circuit need the same protection? Because, except for severely damaged cables, a properly installed hardwired EVSE will have no exposed conductors anywhere except where the EVSE plugs into the car. There is no plug to be only partly in the receptacle. There is no receptacle to get wet before you plug in the EVSE. So the chance of a problem before the EVSE's own GFCI detector is very, very, very small. Maybe not zero, but a lot closer to zero than with a plug/cord connected "travel charger".
The best part is that by the time you add up:
- GFCI/breaker (often $100 or more above the cost of a simple breaker)
- High-quality receptacle (daily plug/unplug means you need a really good one)
- "Travel" EVSE
you are actually close to the cost of a hardwired EVSE (e.g., Tesla Wall Charger)
If you already have a "Travel" EVSE, use it as designed - for travel, so that you have something to use if you visit a location that doesn't have any hardwired EVSE. Plus the hardwired EVSE is always ready and therefore easy to use - just plug in one end (the easy one, at your car) and not "pull it out of the trunk, plug in both ends".