There are actually rocket-based vehicles like that already, although they're typically based on existing armored car or APC chassis, like the Soviet BRDM-2 scout car, the French VAB, and more modern examples like the Stryker
The French replacement for the ERC and AMX-10 RC also ditches the big cannon in favor of a 40mm autocannon and missiles, so it seems they've come to a similar conclusion too, although the whole vehicle is still pretty big (but I guess with modern infrared optics, being small doesn't really do as good of a job at hiding you anymore).
There are actually rocket-based vehicles like that already, although they're typically based on existing armored car or APC chassis, like the Soviet BRDM-2 scout car, the French VAB, and more modern examples like the Stryker
The French replacement for the ERC and AMX-10 RC also ditches the big cannon in favor of a 40mm autocannon and missiles, so it seems they've come to a similar conclusion too, although the whole vehicle is still pretty big (but I guess with modern infrared optics, being small doesn't really do as good of a job at hiding you anymore).