How about the cost of moving the platform to an intercept orbit promptly enough to address a pop-up target? Either you have many of these things in orbit everywhere (expensive, likely to cause great geopolitical strife) or you are invoking stupendous deltaV to fulfill the maneuvering and time constraints necessary. Probably more than is physically possible. If it is, hideously expensive.
How about the upkeep of a chemical rocket in vacuum for a sustained period of time? Spaceproofing anything makes it expensive. If something breaks, it's broken, no ordnance maintainer is available to safe it and start pulling panels.
How about the problem of entry-hardening an exquisite fusing and guidance system that has to decel from orbital velocity and strike a small target moving at hypersonic speeds? How do you cheaply engineer a heat shield around that? Consider the CEP of a MIRV, traveling at suborbital velocity, targeting a static target. Extrapolate those parameters to the level of shielding and precision necessary for an intercept vehicle. Is this purely a midcourse, exo concept?