So until recently I never gave Rex Campaign much of a chance. Why include this blatantly inferior robot when you can have the sexbots? That was true until recently. This card isn't for HB, it's for NBN. Specifically Spark.
Rex has all sorts of things that Spark wants. It's an advertisement. Low rez cost makes rezzing aggressively to proc Spark's ability viable, which isn't true of Adonis or Eve. Its trash cost is decent, especially when you consider Spark tax. You don't even want to bother protecting it because if the runner trashes it you're ahead, meaning you can put your ICE on things that matter.
There are two downsides with Rex in Spark. Influence is a concern, but two is not horrible to deal with. The real issue is that it takes longer than other advertisements to give a return on your investment. 3 turns on the board is not short.
In summary, you have to be willing to play a card that says "the runner loses a click and 4 credits" just as often as it says "delayed hedge fund/make Valencia sad". I personally am because I'm a terrible person, but your mileage may vary.