Personally I take public transit to the airport if it is all possible but I know few Americans who do it. Despite the silly airport trains I think the BART at SFO and the JFK connection to the NYC Subway are great. The train to Reagan airport in DC is is nice as the train to Schiphol airport. Also there is a premium shuttle bus from LAX to Downtown LA which gets you to Hollywood and many other places on the Metro, you can certainly find a good hotel near a transit stop and limit how much you need to lug luggage.
When I lived in SF proper I would take BART to/from SFO. Now I live mid peninsula and then Caltrain/Bart transfer timing is often terrible. That trip can vary from 30 to 60 minutes of transit + 10 min walking. So depending on how it works out, I'll often Uber instead.
It depends. If I was going to a conference at the Moscone center I would take the BART. If I was going to go visit friends in San Luis Obpiso or go see the redwoods I'd rent a car. Most of the times I've flown to Montreal for work I have taken the excellent 747 bus (always stayed downtown or one subway hop away) but I have had times when the hour was crazy late or I hurt my foot and then I take a cab. To the extent that I can I plan the trip around taking transit.
So far as traveling with kids I'd say that many kids who grow up in suburban and exurban areas are driven around in cars all the time and taking the train is more of a special thing for them. Driving and parking is atrocious in Boston or DC so even as a motortourist visiting the region I am inclined to park my car near the end of the commuter rail line and ride in with the possibility of staying in a hotel on the outskirts or one further in.
There is the issue of traveling light or not. I travel light, some people might need to bring a lot of clothes or sporting gear or maybe a CPAP Machine and an Apple Vision and a lot of other stuff but I usually travel out of a backpack. Because shopping sucks where I live it is not unusual for me to not pack extra underwear but buy a bag in town and stuff it with underwear from the Nike store and other items I can get from shops in the city.
Right now I am planning a trip to see the New York Red Bulls play soccer in Harrison, NJ. The PATH train goes right there, it looks very low stress to take the bus from home to midtown, catch a train, spend a night in a hotel somewhere, go see the Intrepid museum, ride home. If I was traveling in a party of 4 or more the cost adds up for taking transit so I would take the car and figure out parking though I would probably design the trip around finding a hotel close to transit and parking just once. Going myself the bus is a slam dunk, even with one friend the bus wins, at three I'd have to think about it.
I'm in a rural location so I am unlikely to take transit to the airport at home but there are times I have. The airport itself has good bus service but the bus home runs a limited number of times a day and I almost always fly in and out early and late respectively. Our local airport has degraded considerably since the pandemic so I think next time I fly it will be out of SYR airport which is about an hour away but is super-competitive almost like a European airport, I am thinking of flying somewhere like Charleston, SC on Breeze Airways mainly because I want to fly on an Airbus 220 and for less than $100 it's a steal. Unfortunately bus and air connections don't work well on this route so it will likely be a "kiss and ride"
I live in Portland where the metro train goes right up to the terminal.
I'll still usually get someone to drive me there. It's a 30 minute drive, whereas taking the MAX is a 10 minute walk followed by a nearly 2 hour train ride.
I'm writing mostly about my experience as a tourist where I can plan my itinerary around transit. You might live in a place where transit is unattractive (as I do) but if you are choosing a hotel you can find one that's convenient.
In one case I was attending a conference in NYC and then going to work in LA so I stayed in a hotel in Queens that was a few blocks from the subway that had a free shuttle bus to the airport. In LA I took the bus from LAX to the downtown and then took the Metro to the Hollywood & Vine era where I stayed at a really cool small hotel just two blocks away. The office was up in the hills and I would catch rides with coworkers to get there.
I'd contrast that to another ill-fated work trip where I went to San Diego and they rented a car for me and got me a reservation at a suburban place my boss really liked that wasn't good for the whole time because ComicCon was in town. Everything cheap was sold out so I wound up at the (great!) Kimpton with very expensive parking (I would have thought the hotel was a fine value if I wasn't paying to park.) Now I came back with a lot of cosplay photos so I can't complain but had I planned it myself I might have just walked out of the San Diego airport to the downtown (unusually this is easy in San Diego) and spared myself that moment of "... damn I don't know which side the gas tank is on in this car."
