Late to noticing this thread...but it is something I now have a bit of inside perspective on, having just joined the ranks of compact system owners.
First question to answer is: No, I don't feel they can or will replace DSLRs, or make them obsolete. The general form factor, including crucially the size, make larger DSLR systems much more advantageous to certain types of photography. There might be a second question, which is whether 'DSLRs' themselves will still be around, or will have morphed into something else, such as Sony's EVF/fixed mirror hybrids or some other hybrid...however the mirrorless compact class will remain just that - a separate class of camera. I can possibly foresee where something along the lines of Sony's SLT system, in a much more advanced and evolutionary form than current, might be the predominant form factor for larger, pro-type systems, while the mirrorless class stays compact and continues to expand in its own niche, probably stealing away entry-level DSLR sales.
As for who's buying them...I can answer that question for myself - a DSLR user who wanted a 2nd system to use as a landscape/wide shooter when I'm out with the long lenses on the DSLR, as well as occasional replacement of the DSLR when I'm in situations where it's less convenient to use or carry. I also have an ultracompact P&S I use for emergency-only use.
What I've discovered surprisingly is that they are pretty well formed already. I expected to find lots of niggling little issues I wasn't happy with, but would accept for the form factor - most notably lack of good manual control intuitively. This was even more of a factor for me, since I was choosing the Sony NEX system - cool, small, nicely built, but seemingly a more obtuse menu driven functionality with only 2 buttons and a wheel for all controls (the Oly and Panny options look to have better external control layout, but I was particularly drawn to the APS-C sensor for the better high ISO abilities, which are crucial since I actually will be using this camera regularly at ISO1600-6400).
However, none of the fears panned out, primarily because of Sony's firmware #3 which seriously overhauled the controls to answer complaints about the menus and buttons. Most importantly, the 4-way controller pad actually has 5 direct buttons (center, left, right, up, and down), as well as the rotational ability for settings. So right off, you actually have more direct controls available than you might expect, with EV, drive mode, flash modes, and Display around the dial. The firmware allowed the center button to store 3 user-customizable settings rather than the default stuff - so now ISO, focus area, and white balance can all be placed there for direct access. The upper of the two body buttons still accesses the menu, for any other settings, while the lower of the two which used to be wasted with 'shooting tips' help screen, now can be user-selected to accomodate the function of choice - I use DRO/HDR settings there. The camera placed in Aperture Priority mode becomes surprisingly quick and easy to control manually - focus can be manual on the lens ring, aperture adjustable by simply rotating the wheel on back, EV, ISO, Drive mode, metering mode, focus area, and white balance all are direct-button accessible, then rotating the wheel to adjust. Half pressing the shutter always saves the settings you just changed and restores the camera to shooting mode, so no setting acknowledgements need to be made. I'm glad Sony made the firmware update, as there is no way I'd have been happy with the original menu/button settings (I bought the camera without the firmware update, so I had a few hours to try it before the change).
So if it shoots equally well at high ISO, excellent res at low ISO, and is surprisingly good for manual controls and intuitive layout, why can't it replace my DSLR all the time? Well, focus is slower. Focus cannot track any motion faster than a person walking. Focusing manually not easy in low light. EVF/LCDs have too much lag and refresh slowness in low light and with fast motion. Shooting stance is less stable/comfortable without an optical finder, large grip, and camera to face. Camera would not be comfortable/stable with long lenses. Battery life can't come close to a DSLR. Lens selection tiny compared to any DSLR system (growing, but will take a long time to catch up to DSLR lens collections which have been around 25+ years). Adapters can be used to work with any lens ever made - but aperture control only on lens and no AF possible...even with newer AF lenses on other mounts. Just to name a few issues.
On the other questions? I'd say on body size they are small enough - but that's me. I don't want anything smaller than the NEX3 as it just wouldn't be comfortable with any lens but a basic pancake. I like how small the NEX3 can be, but can still reasonably be handled with a lens 3-5 inches long. I agree the bodies shouldn't bother to get bigger though - no size advantage over DSLRs, and also likely losing the advantage of the mirrorless design in accomodating other lenses through adapters due to the registration gap being so small. Price-wise - they can be competitive - at least on sale. My big temptation for getting the NEX3 was the fact that I could get the camera and 18-55 stabilized lens for under $500.
Though to answer one thing about taking photos with the mirrorless cams, as far as stance. As REX said, I also don't like the stance of holding a camera away from my face and looking at the LCD. However, I have found the NEX, with the tilting LCD pointed up, becomes a surprisingly comfortable and good waist-level shooter...which is primarily how I've taken most shots with it - good for landscapes, candids, etc.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses