The main point of failure, and in my opinion the largest disadvantage of dynamo vs battery lights, shared by both hub dynamos and side wheel dynamos is: wiring.
The wiring on a bicycle is often very fragile, and in my experience it is always the first thing to break on any bike. This is especially true if you park in a bicycle parking area where your bike is subject to other bikes falling over or otherwise being mishandled by other people. Add corrosion of the connectors in wintertime (salty spray from the wheels) to this mix, and you understand why dynamo lights are not reliable. The frequent movement due to steering of the wire as it crosses from the front fork to the frame can also be a frustrating point of (intermittent) failure, that can be especially hard to find.
The rear wiring is especially vulnerable due to the length of the wire to the rear light (in case of a front dynamo, which is most common here) and the messy wiring that goes with connecting the light across the frame and rear mudguard. Some bikes use the frame as a conduction path (grounded frame) which at least eliminates one wire. This however requires conducting mudguards for rear lights and has the disadvantage that corrosion of the connecting points is common and leads to a gradual decrease in light output. The connection between a rear light and the metal mudguard is a notorious example of this. This also explains why bikes with a front side wheel dynamo and dynamo powered front light, combined with a battery powered LED rear light were very popular (in Europe at least) until a few years ago. This setup at least removes some of the major concerns (no more wire breaking due to steering, fewer connections and fewer and shorter wires)
There have been a few improvements in making more reliable wiring, such as integrating conducting strips into the mudguards and using semi-automotive type connectors that should make the wiring more reliable.
I would prefer to use dynamo powered lights on my bike, as I tend to forget my LED lights when I need them or forget to charge them, but the poor reliability of the dynamo/wiring combination prevents this.