Well LF, while more shots without changing batteries for you and a faster speed on continuous shooting are unimportant for you, they are important to many of us.
Moreover, I wouldn't describe having a grip gives a different feel to the camera, but a different utility, which I'll explain.
If I may, I'm going to go through the reason I use a grip, one by one.
I'm primarily a travel photographer. I can easily take a couple of thousand shots per day, sometimes many more. If I use the small battery which goes in the camera, I have to change batteries, and it's invariably at the wrong time, so I prefer the grip and its larger battery.
I shoot a lot of wildlife, and also events. Shooting continuously at high speed can help a lot. Moreover, when I'm shooting a crowd shot for a travel layout, etc., being able to rapidly take many photos pays off in having a shot where the majority of people in the crowd look "right."
While I shoot the majority of my work in landscape orientation, I do a lot of work in portrait orientation too. I can't tell you how much having the grip's controls and shutter release for portrait orientation helps, not just for ease of access, but to hold the camera/lens steady, especially when you're handholding with a larger and heavier lens.
Finally, the feel question you alluded to must be answered. There are two size issues with which the grip helps photographers. The first is weight. I really don't like the balance and heft of the camera when you've got a longer lens on it and are handholding. The 70-200mm is a perfect example of a lens for which I find the balance of the camera is superior with the grip, and the heft or weight added by the grip helps keep everything steady.
The second issue is the physical size of the camera. I find the height of the camera too short for my taste. I don't have large hands, and I think those with large hands would find the extra height even more useful than I do. With my finger on the shutter release, the palm of my right hand rests against the grip. That's really helpful in keeping the camera/lens steady.
So there you have it. Put those features together and the price of the grip, as inflated as I think it is, is still very much worth it to me.