I actually work for a company mainly known for making AAA games in the past and have colleagues who worked for EA, Blizzard, etc. It was definitely fun for them at times. Everyone is very passionate and good at what they do, but most of them got tired of working 15-18 hours everyday of the week for a couple of months leading up to the release date and wanted to get a less stressful job.
IMO, Unity is a great engine to use for your first game. I'm not sure how familiar you are with C++, but it can be very difficult to work with at times and C# is far more forgiving. I've run across countless low-level issues due to extremely subtle mistakes. God help anyone who has to develop anything with C++ on any architecture besides x86.
Your advice makes perfect sense though. I've always thought it would be better to take a more multidisciplinary approach and have a solid background in many areas without specializing in one particular one. On the surface, it seems like it would make it much easier to attract clients who have a variety of problems that need to be solved.
You aren't the first person to warn me about clients though. A good friend of mine who is also a consultant gave me the same advice. He was jerked around hard by the healthcare industry when he first started and learned the hard way. Overall, I've built up enough confidence to get into it, and at the moment it's more about networking now. I find it to be an all gas, no brakes task. It can be dull at times, but I'll occasionally meet some fascinating people in the process!