As a gamer exclusives sicken me, and should any true gamer since it limits the audience of great games. But since you brought it up I'm assuming you mean console exclusives only. And the list for the 360 is more then just two franchises, some that come to mind are Alan Wake, Fable, Forza Motorsports, Crackdown & Mass Effects (thankfully though that is going multiplatform unlike Kotor).
Exclusives sicken me as well, because whether it is console or PC, someone is missing out. But companies have their greasy hands too deep into it and have no will to let go.
Alan Wake: Fell short of what it wanted to do, failed horribly.
See: Amnesia and Penumbra for well made horror games.
Fable: Only Fable 2 was exclusive to the 360, and I enjoyed both titles. I'll give you that one.
Fable 3 is coming to the PC.
Forza Motorsport: Microsoft's attempt to compete with Grand Turismo. Whether or not it succeeded or failed I do not know as I played neither series.
Crackdown: Played the first one and enjoyed it, never got to play the second one.
Mass Effect: Was only exclusive to the 360 for a year or so.
However most of the 360 games are also ported to the PC which makes having a PC/PS3 combo the best option excluding any interest in arcade games.
This is what is holding gaming back. Developing games for 5-7 year old consoles for games of today. I'm not asking for games to look like Crysis and play like Amnesia, but it is ridiculous how much the consoles are holding up gaming from moving past this silly standard they've set up. Don't even get me started on the Kinect.
You seem to be confused about what is fact and what's your opinion. You are right about Microsoft's faulty hardware at least in the early generations which they paid dearly for and earned a stigma that's likely not going away anytime soon. However the latter generations don't seem to fall into this category.
Everything else is just your opinion on the matter. I find many things to be overrated and in my opinion crappy, that however doesn't make it true for everyone.
I'm pretty sure the faulty hardware persists 'till today. They've done NOTHING to fix their consoles except remove the red LED light from the latest iteration of 360s. It will most likely still have a ~40% failure rate on top of its tendency to scratch disks when the console is in use. God forbid your console gets bumped while you do silly dances in front of the Kinect when playing with your friends/self, or your dog decides to brush against the stand, or your drunk uncle decides to stumble around the room.
The 360 has a lot to offer and many are obviously happy with it. Just because you personally don't find any value in it, doesn't make it to be universally true. Hey I personally think a PC is the best value but saying that usually gets me labeled as a PC elitist. I have a friend who finds his 360 to be the best home for shooters with franchises like Call of Duty, Battlefield, Halo, etc even though not all of those are exclusives. At the end of the day its just up to what fits your needs best.
Ignorance is bliss.