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.
IMO the most compelling machine pistols are those with small light weight folding stocks, not entirely unlike what what the Uzi had. Machine pistols could only be the optimal weapon if anything bigger wasn't an option, but my main point is that automatic weapons are considered relevant to VIP protection by the trained experts, contrary to the musings of internet commenters.
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.