We replaced two doors two years ago. One door is an odd design and the replacement had to be a custom job, so we hired a custom door shop: a local owned business. The other was a front door with a side light. We used Home Depot for the front door.
I found the people who worked at Home Depot to be very annoying, but I really like the door and the price. The two men who installed it were great

. We were even quite a PIA to them as DH was drilling holes through the frame and bottom of the sidelight for the alarm sensor. They weren't thrilled with it, but were tolerant and happy to receive a well deserved tip. Even later (prior to tip) when the work was done they were very friendly as we struck up a conversation. They gave us a lot of extra tips about the door and even a few that involved "be sure HD does this or that because they won't if you don't stay on them".
The custom door place, on the hand, did only a fair job. They ended up making three different visits because they ordered the wrong parts. The door still doesn't close perfectly. We have to give it an extra nudge to be sure it is shut all the way.
So, basd on my HD experience I would say go ahead. I'm sure a lot depends on the store.
We have also had counters installed by HD (subcontractors). That, too, was a good experience. There was a problem with the deal. HD advertised one thing and subcontracted place said it wasn't valid. HD made good on it and actually gave us a better offer than the original. The installers were fantastic and their company followed up twice to insure we were satisified.
To be honest, of the home improvement projects we have done -- we have been satistifed more often with the HD installers than the local companies. (Although, a couple locl compnaies have done good work.)
From what I have read, we are not the norm on a national level. But, I would ask in YOUR area about local experiences.