So what is the point of making 7200rpm drives?
Sequential read/write speeds in HDDs scale according to the data density. If you can write twice as much data per linear inch, then the sequential speed doubles. RPM affects it too, but to a much lesser extent (data density has increased over a thousand times in ~25 years, while RPM has only increased about 4x).
Random read/write speeds in HDDs scale according to RPM. The average random speed is limited by the time it takes to move the read/write head to a different section of the platter. On average, a "different" spot on the platter is a half rotation away. So you move the head to the proper track, and have to wait for the platter to rotate 180 degrees.
A 3600 RPM drive spins its platter 60x a second. So a half rotation takes 1/120 second. A 7200 RPM drive spins its platter 120x a second. So a half rotation takes 1/240 second. Its random speeds are 2x as fast as a 3600 RPM drive.
The bottleneck on HDDs are almost always the random read/write speeds. A good HDD could hit 150 MB/s sequential speeds. But its 4k random speeds were usually down near 1 to 1.5 MB/s (240 random sectors per second * 4096 bytes per sector is almost exactly 1 MB/s, and you could improve it a little more with NCQ, which rearranges random read order so nearer sections of the platter get read first). Before SSDs arrived, Increasing RPM was the only way to improve the random speeds.
For playing back movies, sequential speeds are what's important. So the RPM doesn't really matter (unless the drive is badly fragmented). Would be a different story if your application were, say, reading/writing hundreds of database transactions to the drive per second. Nowadays, anything that needs high random read/write speeds uses SSDs, so HDD RPM is kind of a moot point.
Edit: BTW, if I'm doing my math right, a 4k Blu-ray holds 75-100 GB of data. I dunno what bitrate they typically use, but if you figure it can hold a max 4 hour movie, then the average bitrate will be around 55 Mbps. Figure this can spike up to 80-100 Mbps during action sequences. So while it will work over your 100 Mbps network, any transient network glitch will cause a freeze or dropout. You would be advised to re-encode your 4k videos to something with a lower bitrate than raw Blu-ray. (100 Mbps = 12.5 MB/s, which is far below the 150-250 MB/s sequential speeds of modern HDDs.)