This has been done but there are technical issues concerning the way in which a slow background self erection process is implemented.
In a vac horizon the self erection is done using pendulous vanes (IIRC); in an electric horizon it is done (IIRC) with little switches with weights attached.
In a purely solid state gyro horizon you don't get any gravity sensing so you have to make a stab at when the plane is straight and level, by using one or a combination of airdata or GPS track/altitude data. IIRC Aspen use the former whereas Garmin use the latter. None of this is hard (especially the GPS version) but it means it isn't completely cheap and trivial.
This for example is virtually useless.