-I get local incentives from the utility that offset the extra cost of a Tesla Wall Connector.
-Not every electrician I've talked to has mentioned the 40 amp max. If I go with someone who doesn't recognize a possible limitation, I risk burning down my house. I was just asking to see what other had encountered.
-Check your tone.
Looking at your panels, I can easily see why an electrician would be hesitant to go more than 40 amps. That entire panel full of 20 amp breakers is only supplied by a 70 amp breaker.
If everything is right, even if you put in a 60 amp breaker(on your 70 amp panel!) and its too much load, the 70 amp breaker will trip and you'll know you've overstepped the limit. There should be no risk at all of burning down your house.
Notably, I see both a 240V dryer breaker in the main panel and a 120V dryer(gas) breaker in the subpanel. This implies that one(probably the 240V) is really unused, and you have at least 30 extra amps of capacity at the main panel(if needed).
On that subpanel there are two 'Furnace' breakers. I wonder what's up with that. I assume they are gas based and only have a fan motor to run.
Not actually looking at the faceplates of the various 120V loads off the subpanel, I could even see nuisance trips with an extra 40 amp breaker(32 amp load), since thats HALF the capacity of the entire panel. I don't even see a 'refrigerator' breaker, which I'm sure is there but unlabeled. Things like furnace, hydro tub, microwave, refrigerator, dishwasher all would have motors and heating elements and when run together might be concerning. If you are lucky they are on opposite legs of the 240V(or the electrician can swap them in seconds to make sure that's the case). Lets for a moment assume they are all on the same side, and take 10 amps each... that's 60 amps right there. In reality, most of them will only take 10 amps for a short period(seconds) during startup, so you are probably fine. And if you divide the loads properly, its 30 amps per leg of the 240, leaving a nice 40 for your charging needs.