I’d say that it would be unnecessary from a gameplay perspective and from a lore perspective wouldn’t make much sense if you thought long and hard about it.
Each factions weapons were designed in the same way the faction itself operated and was known for.
UNSC - humanity was always known for being blunt, straight to the point, and didn’t really cut corners so much as they took a frontal approach unless it was absolutely necessary to act differently. So having weapons that did crap shield damage but ultimately devastating flesh damage made sense. They would tear down defenses as long as it took to hit the core dead on with all they had (I mean, Chief even literally threw the Covenant’s own explosive into the reactor chamber of their own ship…doesn’t get anymore direct than that if you ask me.). Pistols, BR’s, SMG’s, AR’s, DMR’s; these weapons were mainline focusing weapons meant to clear the battlefield in a frontal approach (with obvious silencer counterparts for silent Op’s). Meanwhile Spartan Lasers, Rocket Launchers, Railguns, Sniper Rifles, Frags, the Stick Det, Shotgun; these were all power weapons designed with one thought in mind: make it feel like you just got mule kicked.
Covenant - the Covenant had always been superior to humanity in the way of technology, this was because they readily had access to advanced tech humanity had little knowledge of even existing (with the exception of ONI who likely knew about several cases of this tech but never shared with the class. Typical ONI.). Radiation, Plasma, and Super Heating Combine Crystalline Shards were the core of the Covenant’s arsenal. This fit them because the weaponry was every bit like how the Covenant were: advanced, dangerous, powerful.
Plasma - was used in a large number of field ready weapons, most notably the Plasma Pistol, the Plasma Rifle (Storm Rifle), the Concussion Rifle, the Focus Rifle, and the Plasma Grenade. It was also used in their vehicles and warships such as the Banshee, the Ghost, the Wraith, and their Battle Cruisers.
Radiation - was used in arguably very few weapons such as the Fuel Rod, the Hunter’s Cannon Arm, and I believe the Covenant Carbine Rifle. It was also available in the Banshee as a Bomb utility.
SHCCS (Needle Shards) - were used in only a few weapons such as the Needler, the Needle Rifle, and a variant of the Shards was used in Spikers and Spike Grenades.
There were other instances of weapons utilizing things like Plasma Energy for their Swords, Gravitational (I’m at a loss for the word here…) units for their Grav Hammers, and of course fire for their Incendiary Grenades but these were rather rare. (It’s also interesting to note that different sections of the Covenant use different variants of their tech; this may have something to do with a respect level and tolerance within the Covenant. Less respected Fleets may not have access to their more powerful arsenal and there may even be groups of dishonored within respected Fleets which could explain why in Halo CE Energy Swords vanished when the user was killed and why FRG’s exploded when the Grunt wielding it perished or maybe it’s just a game mechanic and I’m overthinking things again)
The Covenant however had different types of tech dependent on the power force using it.
Elites - used Plasma and Energy tech
Brutes - used crude bludgeons and bladed tech (Brutes also didn’t have energy shields to begin with)
Prometheans - use the sheer power of their creations from many generations of advancement. The Forerunners were one of the top most advanced races only seconded by the Precursors. Their weaponry is raw energy tapped from Hardlight material. This fits because they were merciless in their takeover of the Galaxy from the Precursors when the Humans were selected to carry on the will of their creators. Through sheer force and arguably a bit of knowledge exploitation, they seized the reigns of control over every living being in the known Galaxy after defeating the Precursors.
Human technology in the current year we know of 2558 utilizes some of both Covenant tech and Promethean tech. There are several guns that have some mixed parts of either weapon on them allowing them to use Plasma based scoping technology and others allow ammunition to take on Hardlight material. There’s even a Warthog with an Energy Shield that can shoot Needler Rounds. So I’d say humanity is no longer in a dead lock with their tech as they’ve seemingly begun incorporating different variations to their arsenal. (whether it’s just game mechanics or lore friendly I’m not sure, I may have even gotten several things wrong)
As a whole; I don’t think the UNSC really needs Plasma based ammunition. They seem to do just fine with typical rounds and Hardlight munitions.