No, I don’t think I’ve ever seen a Subaru damaged by towing, but then I don’t think I’ve ever seen one used to tow anything more than a 6 foot utility trailer. Overheated fluid kills transmissions, I’d definitely have one installed–a few hundred vs. thousands for transmission repair/replacement seems like pretty cheap insurance. I also think that 2.5 would work pretty hard to keep highway speeds.
You’ve got electric brakes on the trailer, right?
According to the website raj posted above, the weight limit is reduced to 1350lbs for hard towing. I’d consider towing over Snoqualmie or Stevens and pulling the hill at Vantage to be hard towing. And knowing what a 2000lb trailer feels like behind a half-ton pickup I can’t imagine the handling and braking in your Outback to feel very safe. Admittedly I’ve never tried it and you have, so if you feel safe enjoy!