Slightly off topic, but I was reading a locksmith talk about how often lock issues are actually caused by sagging or warping doors, and that often the problem is really a worn hinge. It occurs to me that in the usual hinges, neither the plates nor the pin are hardened, and there are no bearings of any kind. There’s just the soft steel pin, the soft pressed steel plates, and some grease.
Are there any door hinges that are made to resist wear and not get sloppy?
Rarely are hinges the problem. Everyone pays attention to the door and the hinges, what most people don’t realize is the door frame is more often the problem. For example. Many people decide to install high security door locks and hardware on their homes, and any locksmith will happily install them for you at a hefty cost. But, think about this a bit before you decide to do the same thing. The majority of doors are hollow core or fibreglass with thin wooden frames. They look great, but one solid kick at the lock and the cheap frame shatters like cardboard. So, ask yourself, does it make sense to install a $600 high security lock and hinges on a $100 on door?
Most if not all door frames are 1/2" to 5/8" thick, and not made of hardwood, usually spruce, pine or cedar and only held in place by a few screws or nails. So any strong locks or hinges are only as strong as the door/frame they are attached to. If you want hinges that don’t sag, and locks that are high security, start with a solid 3/4 to 1 inch hardwood frame, securely bolted/lagged to the sub frame then install a solid hardwood door. Your locks and hinges will outlast the house and defeat most would be burglars!
That’s true. I’m often surprised that door frames don’t get broken in shipping.
But when they are installed, they can be reinforced, as you say. I don’t know how to reinforce hinges.
I don’t really want more security. I just want better hinges, on principle. They are badly engineered. 
We were often asked to fabricate custom slab doors out of exotic woods. If a client was spending 7 figures on a remodeling job - they certainly did not want doors off the rack from Home Depot. Big (say 3 x 8 foot x 2.5 in thick) solid wood (I recall some ones we made from purple heart) will require big hinges preferably with ball bearing races. While Baldwin is now made in China - they still make decent solid brass ball bearing hinges:
Here’s an example:
But you can also buy ball bearing hinges in much less expensive styles like these:
Those are very visually distinct, with the bearings making little “bands” between the hinge “fingers” that come in from either side. I recognize having seen this style of hinge on commercial (mostly hospital) doors quite a bit.
Is it as simple as that? Look for the bearings?
Those “fingers” as you call them are more often referred to as “knuckles”. In a conventional hinge - if they are installed correctly (not skewed or misaligned) the weight of the door should be distributed pretty evenly - with each knuckle carrying its portion of the load and wear occurring where the metal ring of an upper knuckle bears on its lower counterpart. This could be steel bearing on (and sort of grinding against) steel or brass bearing on brass in the most typical hinges. The hinge pin acts to keep the hinge together and in alignment. A little bit of lubricant might make the assembly turn smoother with an older steel hinge if oxidation (rust) has set in on the pin or hinge itself. Adding a ball bearing race - means that instead of one knuckle sliding/grinding on another you have upper and lower knuckles in contact with a bearing.that rolls. For heavy doors or ones that are in nearly constant Use (your hospital example) this can translate into much smoother action over long time use.
While on the topic - and to round out the tutorial on door hinge styles - there are also self closing (better called “assisted closing” hinges. The styles that you see most frequently may also be called “bommer” hinges - but “Bommer” is the name of the guy (Lorenz Bommer) who did a lot to perfect the design. The company that he founded in 1876 still produces them - but lots of others do as well.
https://www.bommer.com/bh/Default.asp?MyPage=Single%20Acting%20Spring%20Hinges
Those look cool, and hide the hinge pin, which might improve security.
But they don’t seem to have bearings. Do they?
Some customers or designers prefer to show off the brass work including the hinges.Picking different hinge finials (other than button ends) like acorn shapes actually accentuate the hinge. Mortised in hinges work better on thicker doors that can easily accept the mortise. Some of these use leaves that intermesh:
https://www.homedepot.com/p/SOSS-1-1-8-in-x-4-5-8-in-Satin-Chrome-Invisible-Hinge-218US26D/302352520
At the other end of the spectrum from decorative hinges - some steel commercial doors come with surface mounted pivot hinges
https://www.doorware.com/specials/help-center/Pivot-Hinges.cfm
If you check 00’:29" you can see two bearings next to both ends (I think), but maybe I am wrong, Fred should approve if I am right. You can email the brand and ask also. I have not install them, once I was waiting in nursery to pick up my daughter and I noticed they have used a rubbery plastic cover between hinges to cover the gap so kids can not put their finger in that gap, it looked so ugly to me as they used three four pieces of that between the hinges, but I liked the idea as my daughters always get hurt because of that gap. I knew there are some self closing mechanism that is to be installed on top of the door (similar to this hinges) and once the door is closed you can not see that. So I got the idea if there is any sort of hinges like that and started to google it and I found this, now I know if I use these hinges I can use that rubbery plastic cover as one piece not a few pieces.