My opinion from both sides of the subject.
On my car, I replaced the entire system, 6x9s in the rear, no modifications other than a fabbed cover for the carpet. 6 1/2s in the front, fabbed sheet metal mount, and a plastic filler. The factory boxes are not so hard to remove if you take your time. There has been information posted here under door locks, power windows, and Bose speakers, if you search.
I installed a Pioneer head unit, single DIN with mounting plate, 4 channel amp under the passenger seat, and a 12 disc changer in the compartment behind the passenger seat. Mine is an 85, I was doing my own installation, but I still had about $850 in it with all of the sales I could find at crutchfield. Two of my Bose speakers didn't work, and the head unit didn't work, plus I wanted CD/MP3 capability. No cassettes for me. :nono
On another guys car, 91, I was able to get all four amps and the receiver unit repaired for about $600 with shipping and labor. He was okay with using a CD adapter for CDs, so the repair solution worked good for him and the system sounds great. Since he wasn't doing the work, the new system and installation from me or a stereo shop would have pushed him over $1000. I let him make the decision.
You can go both ways, just depends on how much work you want to put in and what your goal is for the final system. You have to remove a lot of interior pieces to install a new system, but you also have to remove most of those pieces to repair the speakers. I wouldn't recommend mixing aftermarket pieces with the Bose system, it can be done, but I don't think you get the same sound quality as an all Bose system, and definitely not as good as a decent aftermarket system. And as SpanishVetts says, you can always sell the speakers and head unit to recoup some of your investment.
Here is the repair shop I used, they offer a three year warranty on amps, one year on the receiver unit.
http://www.carstereohelp.com/
There are also people on this forum who do repairs of the amps.