Amazing Metroid GIF. This thread keeps on giving.
I'm not sure what you mean about firing range and aggro range. the way the game works now is your bullets won't hit anything that's more than just a bit off screen. the bullets despawn shortly after leaving the screen.
I mean it like this:
The PC stands on an elevation. Below it stands the enemy, outside of the traditional 45° arcs but inside the "free-firing" area.
Now, unless the enemy has a ranged "free-firing" attack, then the PC can obliterate and thus farm the enemy with no fear of retaliation. Even if the enemy can fly, climb or jump to the PC the player will be able to deliver a constant stream of damage while the enemy approaches. If you designed the encounter around that, all is well. If not, ...
Especially if the PC has special ammo, is ghost-boosted or has enough time to charge the initial shot this might be a b*tch to balance since it'd mean energy tanks, ammo, whatever else the enemy drops will become far more common, at a low risk to the player.
If the enemy fires projectiles at fixed arcs like the spiny mutant thing from your trailer, then there is a space where the PC can stand and hit the mutant without being hit in return unless the ground is completely even and no platforms are available.
If the enemy does not react to damage by charging the PC, but only if the PC gets "within aggro range" then the PC can just kill the enemy from outside that aggro range. You have played Metroid games, I gather. Imagine Shriekbats hanging off the ceiling. In 2D, the only way to attack them was go below them and shoot them while they fall towards you (or GTFO quickly).
Going back to Ghost song: Since 45° attacks are possible you can do some "strafing runs" from outside the shriekbats "aggro range" to attack it, but if you can plant yourself anywhere near you can just conveniently murderize it without danger to your person. Even if it fell upon receiving damage it would not pose a threat at all. It would likely be shot to sh*t while falling down anyway.
Or enemies that jump as a means of locomotion. Annoying to hit and possibly a minor threat with fixed-arc firing, but a cakewalk with the free aiming mode.
Another thing is if the PC is stuck in a pit around the PC's height and enemies are walking around above. The fixed arc player will have to jump or do strafing runs. Jumping would mean exposing the PC to danger, forcing him upwards through one-way walls or generally alert the enemies if they do LOS aggro. Strafing runs against retaliating enemies would at least allow you to pick your fights by drawing one enemy into the pit at a time. With free targeting the PC can just scooch back from the walls a bit and annihilate all enemies.
This also applies to giant grub bug thing. It would need a serious HP boost with free-range firing enabled. Run away a bit, aim at eye, lay into the bug, repeat until bug is dead. Booring. Compared to the excitement of hopping around and delivering only a handful of shots into the eye every time the entire encounter plays out differently. Assuming the eye is a weak spot, of course.
Advanced players will likely master planting themselves for a fraction of a second and delivering a short burst of damage without losing too much overall mobility. "Normal" players will struggle with this, making encounter design a hairy mess to balance.
Basically, you'll allow the players to snipe. They can deliver damage to specific targets regardless of their movement with nearly no misses, leading to higher damage throughput or at the very least a "free" first high damage attack. This will complicate the design for you and lead to almost all enemies requiring a good amount of mobility and/or attacks with accompanying AI tweaks.