A transformer can help and could also make things worse. I have some bad experience with this.
The way that a radio is damaged by static is simple:
Something charges up to a high voltage, and then there's a sudden breakdown resulting in a high voltage on the first transistor of the receiver.
This can happen in a few ways:
A long-wire or monopole type ...
Assuming that power losses in the transformer are acceptable, and that it's placed after 1:1 current balun (which eliminates common-mode current), is there any reason why it might be a poor solution?
Well, the assumption about loss may not be a great assumption to make. It takes a substantial core to avoid saturation and overheating even at modest transmit ...