What car is this? A VW will look almost new after 100,000 miles in the northeast. A Dodge will look like the rust was a factory option.
If you are paying cash, there's no reason to buy new. If you are financing, a used car might be 10 or 20 dollars cheaper a month making it a no brainer. But not so much when paying cash. A car with 30,000 miles on it is practically brand new anyway.
Fuzzy math? For a 2014/2015 car, you're looking at somewhere between 20%-35% depreciation or more. $20 a month comes out to $1200 for a 60 month loan, which is way less than depreciation.
As a practical matter, buying a brand new car is almost always the worse decision but it's one that many people enjoy doing. Like I said earlier, if I was buying a Honda Accord, it might as well be new because they are well optioned for $25k and hold up their value well for a car. Another obvious example would be a Tesla Model 3 (or Chevy Bolt) where you don't have an alternative but to buy brand new.
Paying cash or financing typically does not matter to the dealership. In fact, their finance (& insurance) office is a profit center so they usually prefer to finance so they get one last opportunity to make money off the transaction. Either way they get paid.
I didn't mention it earlier but IMO MY2014 is currently the sweet spot for a used car. You'll see a lot of lease returns, and most are good enough to enter the national CPO program. You're typically getting a car on the current platform unless it was just refreshed in the last 2 years. You've avoided the worst of the depreciation hit (years 1 and 2) and if you prefer peace of mind, CPO cars are new enough to have fairly low mileage and a decent warranty.
Finally cars have been jam-packed with technology for the past few years so you'll probably get a fair amount of that. However, some of the interesting stuff is still on the horizon (i.e. ubiquitous all-electric drivetrains and autonomous driving) so I see current cars as a holdover until the future arrives. In practice there's probably not a heck of a lot of difference between a MY 2014 and 2017 car in most cases.