A better range improvement for the Battle Hawk would either be ER Mediums in late Clan Invasion/Civil War/Jihad era, or Medium X-Pulses in the Republic/Dark Ages era. The Battle Hawk BH-306 variant from 3067 flips out the medium pulses to ER mediums, kicks in a Streak 4, and a light engine for only another 155 BV 2 points. That increases firepower, survivability, and range to deal with Clan and IS opponents.
The stock Battle Hawk also works well against IS and slower Clan mechs, as well as battle armor and vehicles. I'd use it as an anchor for defensive light scout lances, bodyguards for devoted electronic scouts, and close range terrain attack. The jump jets are a nice addition to allow the Battle Hawk more manuverability.