There are really 2 issues at play here; first is the less than adequate wiring system and the second is the lack of amperage available via the stock alternator. When the cars were new and all of the connections were bright and shiny, the alternator probably did ok but I doubt it because even back in the day the lights would dim at idle, at least the cars I had that were 4-5 years old did.
Because the wiring in many of these cars is aged and the HL circuit is lacking, it causes issues trying to push enough power to them while at idle and not get the circuit hot, therefore it is HIGHLY advisable to run your headlights off of a relay which then takes all of the load off the switch which allows the HLs to stay bright. Also, many people decide to add Halogen or even LED headlights which tend to draw more power (halogen specifically) which then means the stock alternator cannot keep the battery charged thus the need for a higher output unit.
As for the alternator itself, they were not bad but barely adequate for what they were put in, however they did work somewhat when new (until you added anything electrical that had any significant draw such as a big stereo into the car). So, with this there are some options; the stock alternator was usually around 60A, Mopar did make a 90A and I believe even a slight larger one for emergency vehicles. Therefore it is possible to up the stock alternator to a point which bolts right in. Also, there are aftermarket alternator from like Power Master that emulates the stock profile and generally bolts right up (I believe).
The other option is to retrofit a Denso alternator which can be had in a variety of sizes but I prefer the 120A in my builds. Installing it is not super difficult, there are companies that make brackets but I have found they can really be dependent on the specific pullies being used. One of the primary upsides of using a Denso is that you can get one from any auto parts store relatively cheaply. They do not really require a lot of new wiring but they do require that the amp meter be bypassed.
Lastly, regardless of what you do, probably the one biggest positive thing you can do for your car is clean all of the grounds, install more grounds (cannot have too many).