A little less random please…

I do enjoy RPGs, and I've played a good mix of Western and Japanese over the years. But the two things that puts me off most JRPGs are the “Random Battle” mechanic and the turn-based battling.
The first RPG I ever played was Secret of Mana on the SNES. This was an “action RPG” where you could see the monsters wandering around the landscape and had full, real-time control over the battle. The next RPG I played was Final Fantasy III and I utterly hated it. This was a random encounter, turn-based RPG and I found the random element totally intrusive. I found myself on edge the whole time: “Am I going to make it the 10 metres to that town to allow my battered party to rest and heal up or is there going to be a “ker-ching” random battle 1 metre before home that will wipe everyone out? Ooh, the tension.” Also, the turn-based battle element was for me just too abstract to invest myself in, and I stopped playing very quickly. While I can see why it's used as a game mechanic I just can't seem to get past my complete personal dislike of it.
This continued on the Dreamcast when I bought Grandia 2 and Skies of Arcadia. Grandia 2 had a similar style to SoM where monsters were visible wandering around and you could choose to avoid them or fight them. It also had one of the best battle systems I've ever played with. It was real-time but with with “cool down” periods for each characters attacks that weren't fixed to turns and a very simple but excellent positional strategy element that wasn't grid-based. Skies of Arcadia on the other hand was a typical random battle, turn-based RPG and once again, despite the superb visual design and story, I just couldn't get on with it.
So, why do some people swear by random battles and turn-based fighting? What is it about this that makes you want to play it? Despite being involved in the games industry for almost 8 years now in QA and Design I simply cannot see how this is in any way fun. I know for certain I have trouble relating the often highly involved and emotional characters and stories in these games to the incongruous, completely mechanical fighting system. They appear to be two different games that met in a car crash. Compare this to action RPGs where your involvement in the characters and story (walking around towns, talking to people etc.) is perfectly matched by your involvement with the characters in battle. The underlying number-crunching is the same, but the presentation couldn't be more different.