This is not entirely correct. The stug(original short barrel assault gun) at least was originally created to provide DIRECT fire support for infantry and maintain close distance to them.
Assault guns in general are supposed to provide direct fire support rather than indirect compared to other SPGs.
The su76 is a bit of an exception to this as it has an extreme amount of elevation to its gun allowing for indirect fire unlike other assault guns such as the ISU152. That said the SU76 often relied on close infantry support to help cover its flanks particularly in urban environments.
But I dont see the point in giving su76 a speed buff when near infantry as its already fairly fast and it would be counterproductive since the Su76 would outrun the infantry even faster.
It not incorrect.
Assault gun where not tank and did not move in close with troops. The fired from a distance where the lack of turret did not make difference. The fire they provided could be direct or indirect.
Stug-E had a gun with high elevation and could fire both direct and indirect fire.
When German where low on tanks and tried to use assault gun as tanks they vehicle failed in the role.
"Assault guns" provide support fire for the infatry to "assault" rather then do the assault themselves.