I am not familiar enough with technical dimensioning rules for valves to say that there is no rules for spindle dimensioning, regarding diameters.
As you are aware of, general rules for valve dimensioning will say something about connecting dimensions and building length, and for some give guidelines of material selections, minimum thickness and strength calculations.
For larger valves special strength calculations and tests can be required from certain authorities, markets or end users. Standardized performance tests will reflect the standard limits for the pressure class.
Back to spindle thickness.
From a stabillity and standtime viewpoint, by my own experience, the practical problem with spindles is the under-dimensioned spindle, rather than the sturdy, precise manufactured spindle, with good and solid bearings, proper sealing and sturdy and solid fastening to the obturator and closing body (ball, clack, disc etc) of the valve.
Any quality valve I have seen have had theese positive features.
A common spindle problem is a too weak (slim)spindle if application (and or construction or maintenance) leaves the valve stuck, and torque increases out of 'expected normal' range.
Good quality valves with sturdy spindles will normally not end with a deformed spindle by this.
Factories normally differ somewhat in spindle dimensions, and for 'normal' serial produced valves may have 'steps' in dimension details, also spindles, that differ from the steps from competitors.
If you take valves for water as an example, European valves are constructed to satisfy a minimum water velocity, depending on pressure classes.
The weakest/cheapest constructions will satisfy the minimum demand, with slim spindles and simple fastening constructions The best producers can, with their standard size of sturdy spindles, be used for far higher speeds. Especially for larger valves (say above 250 mm?) even more sturdy spindles with even higher diameter might for some factories be a factory option.
Norms, and lacking norms for actuator mounting (spindle top and top flange construction and measurements) could fill a book for itself, but some norms do exist, as you probably know.