Why there are so few lenses with small minimum focus distance?

Because most interchangeable lens cameras typically use larger-format sensors than 1/2.3"-format.

The close-focusing capability of most small-sensored compacts comes from the fact that small sensors use proportionately short lenses. Very short lenses (those under 10mm focal lengths) tend to have very deep depth of field--deep enough to have close focus capability. "Macro mode" on a P&S camera is simply changing the focal distances the camera will search through. While your SX60HS has an "equivalent" focal length of 21mm at the wide end, the actual focal length of the lens's wide end is only 3.8mm.

A four-thirds (4/3"-format) or APS-C format sensor is roughly 4 to 6 times larger than a 1/2.3" format sensor, and requires lenses that are 4 to 6 times longer. The longer a lens is, the thinner the depth of field becomes at similar aperture settings, and the larger the minimum focus distance gets. This is one of the tradeoffs of using a larger sensor. And it's why you don't see macro modes on interchangeable lens cameras.

The focal length of a lens is a calculation made when the lens is imaging an object at infinity. This is a distance as far “as the eye can see” symbol ∞. As we focus on objects nearer than infinity, we must lengthen the distance, lens to sensor (film). The now elongated distance is called “back focus”. The lens to sensor/film extension becomes large. As we focus to achieve “life-size”, often called “unity” or 1:1 magnification, the lens will be racked forward 1 complete focal length, and the distance object to sensor/film will be 4 times the focal length. What I am trying to tell you is, the amount of mechanical extension to reach magnification 1 (life-size), is one compete focal length.

So, to make a lens close focus and reach unity requires lots of room to rack the lens forward. This is actually not too difficult, but now for the rest of the story. The f/numbers we know and love, that are engraved on the lens, are calculated from the infinity focus position. As we close focus, the engraved position marks for the f/number settings become invalid. At magnification 1 (unity), the error is 2 f/stops. This is a problem because we tend to underexpose when we close focus.

This f/number error is called “bellows factor”. If the camera reads the exposure measuring thru-the-lens, bellows factor is not an issue. If the exposure is determined by an external light meter, it is a big problem. As rule of thumb -- most camera makers (lens makers) stop the forward travel of the lens when the bellows factor error approaches 1/3 of an f/stop. The macro lens design is clever in that the lens array portion ahead of the iris diaphragm is a strong magnifier. As we focus close-up the magnification makes the diameter of the aperture opening appear larger. This magnification of the aperture allows more light to transverse the lens. This is how the macro design nullifies the bellows factor error.

Naturally it costs more to incorporate this design; so many lens makers stop the forward movement as the bellows factor approaches 1/3 f/stop.

A further consideration is that most macro work is (partially) front lit. This gets harder to do the closer you get to the front element. Even ring lights have a minimum useful distance imposed by geometry. So a focus touching the front of the housing is rarely useful. While hard to build in to a lens with infinity focus, it's easy to active with a bellows or extension tubes for those occasions when it is required.

Even microscopes used in transmission mode have some working distance (often less than 1mm, and ignoring immersion objectives).

The minimum focusing distance for compact cameras tends to be for the wide end of a zoom lens. The magnification of a long end zoom needs strong lens elements, and focusing to short distances also needs strong lens elements. Different zoom lengths are achieved by rearranging the existing lens groups. When the arrangement does not need to produce a long zoom length, it tends to have some leeway for producing a short focusing distance instead, at least when assuming a non-parfocal design (which most compact cameras have).

To get reasonably short focusing distances for closeup work at the long end of compact zoom cameras, you usually do need additional closeup lenses in front. Why aren't they "built-in", so to say? Because you cannot just move them aside when you want to focus on infinity: the camera changes its view only by rearranging the positioning of the existing groups but cannot change or disable their individual effects.