That might work in warmer climates (and 120 V charging is also wasting quite some energy), but not if it gets really cold. With little over 1 kW available to warm the battery it would probably take all day long just to be able to actually charge.
Right now it's -23°C (-9 F) where I live and I wouldn't want anything less than a 240 V / 48 Amp setup. At least I'm not draining my battery while the motors draw some 7 kW to precondition the battery.
It takes nearly three days to do a full charge on a long range Model 3 or Model Y. The remaining time in the day (which is several hours) you could drive about 250 miles on what you've charged. 365 days in a year means 121 full charges. 121 full charges means 30,250 miles.
And that's with loads of buffer time both for required charge time and available drive time.
Of course you could also just charge and drive as much as possible on a daily basis, or however much you need. But the trick is to "ABC", Always Be Charging. If the battery is full it's time to drive. If you're not driving, plug it in.