A 'Y' capacitor* from secondary to earth would be rather undesirable for a floating item of test equipment. When you initially make a connection from secondary side 0V to a ground referenced circuit, there will be a nice zap of current to charge/discharge that capacitor to the new potential. Not exactly desirable for a supposedly floating instrument.
That's why I specified an inter-winding screen, as the only way to return the HF leakage current from the inter-winding capacitance between the secondary and the 'hot' (switched) end of the primary whence it came without compromises# is to intercept it with screening before it reaches the secondary. Once you've got the screening, it might as well be grounded to minimize line frequency leakage current. Unfortunately inter-winding screens cost core window area so push up the size, weight and cost of the magnetics so are usually only seen in medical rated equipment, and purpose designed PSUs for precision equipment, where the extra cost is a minor factor.
* Is it a Y capacitor when it doesn't have to stand off line voltage, even if the part you use is rated as one?
# See above, & also, the leakage current causes bad things happen to sensitive devices under test if your suggested grounded secondary side, or grounded Y capacitor SMPSU ever looses its ground connection.