Most GC's do NOT have the skill to install cabinets. It's a specialty skill and much more involved that you think it is. A good installer can take 10K worth of cabinets and make the kitchen look like 100K. A bad installer can take 100K worth of cabinets and make it look like 10K worth of crap.

If a GC is flexible, you can hire him for just the construction type issues that you may need for the project like taking walls down etc. If you're not doing anything that involved, then you may save some money by acting as the GC and hiring the individual trades yourself. If all you are doing is replacing the cabinets, then all you may need is a cabinet supplier and installer.

I had a different experience. My kitchen designer works with independent contractors who specialize in kitchens and as well as general contracting. He was available to work with the GC to discuss certain design elements and guided the design. They often argued about functionality/cost versus appearance. The kitchen designer often recommended expensive options and the GC executed realistically. For example, I installed glass counters and wanted ss for a substrate. The designer just went to the fabricator and came back with a cost of 1200 for the SS substrate. The GC did it himself for 250. They worked together to design my base/crown/frame moldings. I was lucky that the GC had one really terrific carpenter who worked for him. The granite and glass fabrication companies did the counter installations. The GC was not great on "pretty" and that is where the KD really helped...wall paint color, etc.

Have you look at any small remodeling companies that specialize in kitchen and bath? Many will have a designer or two on staff and since they only do kitchen and bath remodeling, you know they are experienced installers.

I am about to start my renovation. My cabinetmaker is strictly for the cabinets and their installation. He doesn't do anything else. His specialty is cabinets. I hired the GC that I wanted and even the stone fabricator that I want. The coordination of the work is perhaps more work for me, but not by much. Email has made all of that so much easier.
I had approached WoodMode cabinets initially, but had to use their GC. I didn't care for him.

So, it really depends on the people you talk to but the options are there.

At my old job e had in house install but ould work with a clients installer or even a DIY, BUT I insisted on meeting ith the installer prior to orderingor even finalizing the design. Sometimes we would need to simplify details to keep them in line ith the skill levels involved.

Being a GC neither qualifies nor disqualifies someone.

In my business now we do not have in house install, rather offer several installers to work for the client, or work with the clients installer- we treat all jobs as if they were in house. Same meeting requirements though.

Some places will only do in house or their on,partly because of oney, mostly to avoid problems