The biggest drawback to the Schwinn design wise to me is the one piece crank, but its not a deal breaker. I put a ton of miles on an old Schwinn Varsity back when i was young with no issues but when I upgraded to a lighter bike with better bearings the difference was very noticeable even as a kid, but my goal then was to go faster not just being out for the ride.
These days the bike I choose to ride is often just the easiest to get out without moving 20 others, often which ever bike I just got done going through.
As I find others, others get pushed farther back in the garage or simply require moving a ton of stuff to get them down off their hooks.
A few years ago my daily ride was a '72 coaster brake Schwinn Speedster. An extra tall frame model, it was just a good fit for me and it got used for the better part of the year, now its behind many others, with a '68 Sprite being the easiest to get at since i just got done going over it.
I've got a half dozen Schwinn's, and as many English models awaiting my attention. Plus a few older rebuilds that are due again after many years of use.
Another downside to the Schwinns is the odd tires, finding good quality tires has been tough lately and most are stuck with cheap tires where as I tend to use Michelin World Tours on my English bikes.
I got lucky with my 62 and 56 Schwinn Traveler models, both came to me with minty clean vintage tires, one with old Uniroyal chain tread, the other with Sears Allstate tires. How they survived I'm not sure but they look and feel like new tires.
I always thought my '62 Traveler would look good with wide whitewalls but I refuse to spend $60 for a pair of Kenda bike tires. The 62 is all black with the one year only Starburst headbadge and chrome fenders with a three speed on S5 rims.
I've owned both of the 62 and the 56 Travelers for the better part of 30 years now. One was a an estate sale buy, the other I bought at a bike shop for $10 while traveling for business. Contrary to popular belief, you can fit a 1956 Schwinn Traveler inside a 1987 Corvette, (in pieces). I found it but was driving a company car and didn't want to leave it or risk shipping it so I took it apart in the parking lot, wrapped it up in paper and stuffed it in the back under the rear window for the duration of the 23 days on the road checking on various company construction projects. The bad is that I never did put it back together, its been hanging on the wall in pieces awaiting a few parts it needed, long since found, and my time.