If you wanted to depict a modern real life naval battle, that would be also be the exact same way of how you would film and shoot it.The anime scene reminds me an awful lot of the Andromeda space battles.
Very rarely you'd see the Andromeda straf a Neitzschean fleet but for the most part battles were depicted on radar screens with drones for close combat, point defence turrets picking off missiles fired from long distances, and shots back and forth between individual shots of each ship but they wouldn't be within the same shot on screen
If you're WVR (Within Visual Range), you probably screwed up as a Captain.
Modern ships aren't designed to fight other ships up close, no modern ship is designed like WW2 ships with super thick armor hulls.
Most modern ships hulls are fairly thin compared to WW2 ships. But that's because the offensive power is so great that CIWS (Close-In Weapons Systems) and Anti-Missile Missile Batteries are used for close range protection.
Best Defense is a good Offense, there's largely no reason to let enemy projectiles get close.