The only features that have been added to Blu-ray players recently, such as screen mirroring and 4K upconversion, are inessential.
Your 4K TV will already upconvert video as well as any inexpensive player, and there are better ways to get your mobile device’s screen to your TV.
Blu-ray discs offer far better picture (and audio) quality than DVDs or streaming services.
For a second room, a Blu-ray player can do double-duty, providing disc playback and adding some basic streaming services to an existing TV. Companies like Toshiba no longer manufacture players, and these days, most of any given company’s models are nearly identical.
It also leaves off features that most people don’t really need or care about, such as 4K upconversion and 3D playback.