The Y chromosome does a bit more than just carry the SRY gene.

There is a condition where a father’s SRY gene gets transfered to the X chromosome of a sperm, resulting in a child who is XX and SRY positive. [0]

In all known cases, such men are infertile. Fertility treatment is the main source of diagnoses for this, as that is typically the only symptom.

[0] This is de la Chapelle syndrome, although that syndrome also covers an even rarer situation of an XX SRY-negative child developing as a male.