Yes, ALL ships should have the ability to display trophies in the captain's ready room. Jem'Hadar, Andorian, Tal Shiar, Romulan, I don't think any of those ships have the ability to display trophies/accolades and it STINKS.
In the immortal words of Captain Sisko: "It may not be what you believe, but that doesn't make it wrong."
I don't care much about trophies, but I agree that all ships should be able to display those.
And not just that: I think it's time that all the special ships get a fully developed interior. It's kind of ridiculous that the most expensive ships in the game (those that come from lock boxes) don't have a full interior, just a small bridge where you can barely turn around (this goes especially for the Jem'Hadar ones).
I still hope that, once there will be more functions added to the ship interiors, those lock box ships will get some attention as well.