On average, this build does roughly ~64 damage per attack sequence with his Pact Weapon while the Eldritch Blast with all of the damage increasing invocations tops out at ~56 damage. Although a big part of this superiority is dependent on choosing a weapon that deals 2d6 damage (hence greats...
An iconic warlock combo is using darkness and devil's sight to get advantage on all their attack rolls (you see them but they don't see you). However, darkness requires concentration to maintain, so you can't use Hex at the same time. If you can convince your bard to cast darkness ...
With War Caster, you can provide the somatic components of eldritch blast even if your hands are full of weapons. With Improved Pact Weapon, you could provide the material components of a spell using your pact weapon as your focus, but eldritch blast doesn't have material...