Additionally, the very long history of machine pistols would indicate the form-factor is a poor fit for the application of any full-auto fire.
This is the primary reason that personal defense weapons (PDWs) were developed in the first place.
someguydave is correct. Compact automatic weapons make sense for highly trained body guards protecting VIPs when discretion is considered important.
Compact automatic weapons still usually have either a stock (even the smallest Uzis do), or some other way to stabilize the gun while firing - e.g. the sling is used for this purpose with some MP5K variants.
As int_19h points out, there are special-purpose weapons made for this (see "personal defense weapons") and they are likely what pros carry.