Would news anchors ever go on strike?

Doubtful, as the network would have no issues finding a replacement, especially one who would work for less money. The era of the trusted journalist who was familiar and welcomed into one's home is over. So a strike would likely violate contract terms and the network would replace.

They're typically not unionized but any job can potentially strike.

only when the anchors have been tossed. they have land somewhere

If their union did, yes.