Starting with blocked-out volumes representing components that are working at #Minamil: a minimal CNC mill and vertical configuration, I've considered a couple of layout ideas:
Perhaps the more sensible & easier to make stiff: footprint about 14 x 20 cm (8 x 6 in)

The more aggressively compact: footprint about 14 x 14 cm (6 x 6 in)

For evidence of progress beyond CAD and hand-waving, here's a three minute video:
The telescopic axis design contributes to compactness when not operating.
Transparent panels for debris enclosure -- sides but maybe not top or bottom -- can fold compactly around the retracted axes for storage. Assessment of ventilation requirements required.
These depictions assume a Dremel-like spindle. Assuming a general-purpose tool that anyone might have or acquire for general use apart from this machine reduces the scope of what "the machine" includes. OTOH a dedicated spindle could avoid making the operating configuration taller, and get closer to always-ready a la stapler, at cost of added cost.
AFAIK the WEN 2305/7 rotary tool I've used so far represents a Dremel 395-type tool and other similar clones. It weighs half a kilogram, as does half a liter of any aqueous beverage. The machine does not include the counterweight. It includes the rigging for a counterweight, stowed inside the basic bounding box, to be set up when needed for operation. The user will provide an ad hoc counterweight as/when needed.
Companion project #Minamil develops the CNC mechanics. This project started as an aspiration to make that project reproducible from a short BoM and a laser cutter. Since then I've shifted toward thinking the working parts (that project) and the frame (this project) should remain separable for practical usability -- at cost of growing insignificantly larger than a tightly integrated unit. As a result, the "short BoM and a laser cutter" emphasis stays with the Minamil mechanics while this focuses more on improvisation-friendly cabinetry.
For the spindle, my machine uses a 5010 brushless DC motor turning a 5mm rod that goes down into a wood block with a big 16x35x11mm bearing at the bottom, which fits around an ER11 extension chuck. Having the bearing so close to the bit gives excellent rigidity. It does cover up the wrench flats in the chuck, but instead of using two wrenches you can just grab the rotor of the motor while you tighten the ER11 nut with a wrench.
But the 5010 motor needs an ESC, and a servo tester to tell it what speed to go, and some kind of power supply to provide appropriate DC voltage for it, so that may increase the machine size beyond what you save with the smaller motor. Also the big bearing on mine gets hot and I'm not sure why. It really should be an angular contact bearing, but unfortunately there are none available with 16mm ID. I'd like to use a C10 ER11 chuck (10mm integral shaft rather than an extension chuck) with an 7000AC (10x26x8mm) angular contact bearing, but then the motor can't turn it directly like the 5mm shaft.
Regarding overall machine design, one thing you might consider is making it usable as a little drill press. Very handy to have around if you don't have space for a big one. Try to make it so you can at least get a 2x4 through with enough side-to-side room that you can drill a hole anywhere in it. And put a manual crank on at least the Z axis. But manual cranks on all 3 axes are wonderful to have, even just for positioning after you get the workpiece clamped down. Also nice being able to do simple milling operations without having to mess around with the computer.