Car owners have "reasonable" access everywhere. Highways are sufficent and parking (whether street or garage/lot) is plentiful even in areas like the North End. So the question is: do non-car owners have reasonable access to the same employment and shopping centers? No, hands down. If we are going to talk about balance and equity we should do so honestly.
Then we can throw on the fact that ensuring cars have what you deem to be reasonable access to the dense core will actually destroy the unique and alluring characteristics of that core itself driving ever greater numbers of residents, visitors and attractions to the carburbs. See: Detroit, Atlanta, etc.
Highways that get congested starting at 6:15 in the morning and don't clear up until after 10 aren't sufficient.
The vast majority of adults have cars, the same argument can be made about cellphones or computers. I have access to a lot more information because I have a smartphone than someone that has a regular cellphone. Like it or not, they're here to stay and essential to modern life. Try going on a ski trip by taking the train (even if it did still go up to Bethel ME), or any vacation with children.
Basically every major city depopulated in the 1960s through the 1980s-- those without interstate access even more so, as trains proved to be inefficient for transporting finished goods. The cities depopulated largely for a few reasons--
forced desegregation/ethnic conflict-- detroit as an example.
removal of reliance on trains/ships for transportation and the cargo container revolution-- which removed the need for keeping factories on the waterfront or near rail lines and made it much easier to move factories to a centralized location to leverage economies of scale-- Baltimore and NYC being prime examples of this
decaying/non-existent infrastructure that hadn't been expanded/built to meet the needs of truck centered supply chains- try running a goods based business in Boston while the old central artery was there.
Consumer preference-- believe it or not, but families with three kids would prefer to live in the suburbs with a lawn, swingset, and quiet road that kids can ride a bike in
Cities have repopulated because of: demographic trends, a shift to a knowledge based economy, consumer preference (by people without children) and relative ease of transportation access.
Chicago has quite reasonable highway access and a vibrant urban core that wasn't chewed up by road construction. The same goes for Minneapolis, Cincinatti, and Kansas City. Grabbing another 50 feet of right of way along I-93 wouldn't ruin those areas, but it would make one hell of a difference in having a functional road system that doesn't require getting up at 4:30 to beat the morning traffic into the city. And you can shout park and ride with transit all you want, but the simple fact is that adds 20 minutes to a commute, which because of insane anti-sprawl laws that raise the price of housing, already requires a 40 minute drive in traffic to the park and ride.
By ripping up those pre-1925 places and installing parking lots and wider roads? Or some other means?
In limited locations it has to/should have been done. There was a lot of insanity in the highway construction era (at one point there was a consideration of creating an intermediate belt between the inner belt and 128 along where chestnut hill ave is), but the system that was proposed was a good medium that provided the best possible system with as minimal neighborhood impacts as possible.
And yes, parking lots sometimes get built, but remember, about 15 years ago everyone around Boston was up in arms about cellphone towers ruining the landscape. Parking lots are hardly an issue here in disrupting the urban fabric versus other places that are 100% car centric like Dallas, Houston, or Orlando.