I think without Supercharger access, the Tesla experience won’t be as seamless.
I would change your "think" to "definitely", but there are some caveats.
Tesla Supercharger, if you are driving a Tesla, is "plug-in, walk-away". (however, I would recommend that you check that the charging-speed is ramping up. On occasion I have plugged into a charger and it has only ramped up to "not-very-much". Disconnect, move to different stall, problem solved. So you do need to check that, but that applies to 3rd party chargers too)
In theory any "pump" brand can check your VIN or MAC or similar and recognise that you have a payment method on file and just start charging. I don't know if any3rd party chargers support that for Tesla cars (other than Superchargers), but others can correct me on that.
My pet peeve: All charger brands could start dispensing immediately for, say, 2 minutes - enough time for you to initiate / pay for the charge with APP. 2 minutes juice is a tiny cost to them, they could have a black list of abusers if they need it. If you fail to make the APP work you will have 2 minutes juice to help you get to another, working!, charger.
So anything else, including non-Tesla cars charging at Supercharger, requires: "Open the APP" (you've already got THAT brand's APP installed, right?
), tell it which stall (maybe scan a QR code on the stall) and initiate charge. That will fail some percentage of times. On occasions you will have to phone up to get the charge started. You may need to use the APP to end the charge too. Using the APP for START and STOP may take several minutes each.
The other thing to consider is how good the charging experience is - Tesla Supercharger vs. The Rest.
There are occasions when The Rest will charge you faster. But not many.
In the majority of cases Tesla Supercharger will have: more stalls, better uptime, cheaper price. And typically it will be mostly Teslas charging there (
some exceptions, like Heathrow where Taxis of all flavours are helping themselves); all-Teslas means that all cars charge quickly (i.e. some other-brands are slow / take forever and/or the Chargers are either "slow" or the chargers are fast but sometimes slow (e.g. in cold weather) and coupled with "lots of stalls", that means that the churn at Tesla Superchargers is quick, and if you have to wait it is rarely for long.
So, bottom line, you will be better off charging predominantly at Superchargers
Tesla gives you a detailed invoice for charging - its a bit of a pain to download 'coz you can only do it from the APP (i.e. you can't just get it by Email once a month), but it might be that you could submit that to "expenses"?