This does not sound viable to me.
Armor and projectile weapons is essentially an arms race. You state that now the armor is strong enough to sustain small arms fire of low caliber.
While this might be true, it wouldn't take long before the weapons systems catch up to the armor. Historically and presently, armor can only stop a certain subset of weapons, but this only causes soldiers to carry more powerful projectile weapons if they are known to face an enemy with this type of protection---it doesn't mean the attacker will switch entirely to melee weapons, not historically, nor today. It seems much more practical to carry a projectile based system capable of inflicting effective damage despite added weight and support systems due to the many benefits this entails. Attacking at a distance is invaluable.
As for the idea that the core is too small to hit, and the statement:
A fight can only be won if you take out either the brain/core or
deplete their energy
This also appears implausible, and there is a logical contradiction here.
If the fight can only be won by attacking the brain/core, and the brain/core is too hard to hit with firearms, then what is it that makes melee weapons so effective? Attacking limbs, motor functions, nervous systems, vascular systems, etc. must also be an affective vector here as this is the premise for why melee weapons are effective. Hence a high powered rifle round or explosive rounds as already mentioned, and possibly energy based weapons, appear a lot more plausible than mere melee combat.
It is also mentioned how vehicles such as tanks and fighter jets exist, it is not clear how melee weapons fit into this scenario considering that.
Just to address some of the comments made by Rum:
You claim that:
"Well armour would be adapting with it and there's only so much power
a weapon of short barrel can produce.What makes melee weapons
effective is that you won't run out of ammo, and you can sever limbs
which bullets can't, that'd lead to exhaustion and thus be fatal."
It seems there is a misunderstanding of how a firearm works and why a firearm is an effective weapon in the first place.
Yes, there is a limit to how much energy (you generally don't refer to a firearm as having power, as in work over time) a firearm can deliver.
However, by your own logic, why would there not also be such a limit for a melee weapon? Surely you're not saying a melee weapon has infinite power?
Then it comes down to a matter of what weapon, firearm or melee weapon, can deliver the most energy to a small area, in a practical manner? Keep in mind that the area where the energy is delivered is of great concern, the pressure is force over the area. If the area is big, the pressure becomes lower, and the damage that can get inflicted becomes reduced down to practically nothing. Conversely, if the area is small, the force can be small, and it can still penetrate. This is why a syringe can penetrate human skin with ease, while a stick would need a lot more force. This is, incidentally, how armor works in the first place, by distributing the force over a bigger surface area.
As an aside, the physics and physiology of damage inflicted by weapons is a complicated matter, and what I've already stated only barely scratches the surface of its complexity. For this reason exactly, it is better to look at history and the empirical data, the present day situation regarding firearms and armor.
So why is it, that with this fancy armor, that a melee weapon is able to penetrate it at all?
A projectile is powered by an explosion, which delivers an incredible amount of force over a short time. How will the melee weapon be powered? By muscular force? By servo motors? By what motor system, and how is this system able to generate more force and inflict it in a surface area small enough to beat a projectile based weapons system?
Then, after that has been justified, we come down to the tactics of warfare and how being able to attack at a distance is invaluable.
Basically, your melee weapons system would need to be so much more effective at delivering damage than a firearm, that it would completely negate the advantage of being able to attack at a distance. I think you would find this exercise in arguing for this to be very hard if you accept the basic premises already discussed.