re. self adjusting:
A ball will tend to center (within limits) in a hole if the ball isn't constrained.
In a ball and hole valve, lack of constraint means play in whatever type of linkage there is connected to the ball. If there is no play, the ball is constrained.
However, the play is not only the means by which a ball will center, but also creates the need for self-centering in the first place. If a ball is perfectly aligned with a seat and the linkage has no play, the valve will be centered when closed
Play (or clearance) is necessary in a vertical ball and stem type steam safety valve, because the valve stem must be free to slide in the tube, despite corrosion, heating effects, lapses in lubrication, etc. Clearance can't be overly restricted. Therefore the ball needs to have a range of movement to self align. And in an internal valve of this sort, steam must also be able to pass alongside the valve stem. An external vertical tube ball type is somewhat better, but the ball must have a restricted clearance range in the tube, which amounts to the same thing.
In a lever type external ball valve any play will be located in the pivot. The circumferential play can be taken up by guides near the ball. Some clearance is necessary there, just as in the vertical tube and rod types. The radial distance is well constrained in this type of valve, but not absolutely so. The pivot will have a tiny amount of play. And to the extent that there is play, there is also the ability of the ball to self-align provided that any misalignment is less than the degree of play available for self-alignment.
Where there isn't enough play to overcome misalignment the ball will enter the hole off center. This will allow the valve to leak, but won't interfere with the safety of the valve. Generally ball valves are "set" by tapping in place to slightly form the seat, in which case the seat forms to the ball and corrects a minor misalignment, and sets a very slight taper in the seat. The same thing is done with a stem and ball valve.
If grossly misaligned, tapping in place won't work. Example: in a stem and ball type valve, If the stem is attached off center to the ball, it won't work. The solution is in carefully centering the stem when attaching to the ball, Likewise for a lever system it consists in properly aligning the lever when building.
Both systems have the same requirements for initial alignment, and both can use the advantage of self centering to a small degree.