Pros and Cons of a washer tray
Looks like you hit the pros and cons of the washer tray pretty well :-) Couple of things I'd consider:

Since the room is tile and concrete, is there a drain in the floor? If so, adding a washer tray is rather unnecessary and I'd leave it out, just ensure that the floor and tile are properly sealed.

(I have seen washer trays that pretty much are the same footprint as the washer, and just raise it off the floor slightly; these blend in very well and would not be as obtrusive as a generic tray, however they may or may not exist for your model of washer, I would start with the manufacturer as they likely have one.)

As for the feet on the washer, most home improvement stores sell small carpet discs to put on furniture legs in order to prevent them from scratching wood floors and such, they also usually have small plastic discs with soft material on them for the same purpose, I'd recommend putting one of those under the washer's feet. Might see if you can find rubber ones, some of the carpet ones are made to glide easily over smooth surfaces, making it easier for chairs and such to be slid around, but you don't want your washer meandering around the laundry room! Although front loaders have a lot less motion/vibration than a top loader so this might not be an issue.