I'll put it bluntly, the game took too much away from the School of Illusion for it to be effective. Too many spells from the classic Illusionist class were removed from play for them to be considered useful to a party used to an Evoker chucking Magic Missile and Fireball out their bunghole every time an Ork appears. I get it that many spells were rolled together into other ones, but the fact is many of these spells have reduced the effectiveness an Illusionist used to be able to bring to the game compared to the average Mage with Fireball.

Example:

1E's 3rd level Paralyzation is infinitely more effective than 5E's 2nd level Hold Person, since the former was only Verbal & Somatic, AOE (20ft by 20ft area), creatures whose combined hit dice do not exceed twice the total level of experience of the illusionist, requires either Dispel Illusion or Dispel Magic (or the Illusionist ending it to release the paralyzed creatures). The latter is Verbal, Somatic and Material, effects 1 creature unless cast using a higher level spell slot and lasts a total of Concentration up to 1 minute.

So many useful spells such as Gaze Reflection, Hypnotism (1st lvl version of Suggestion), Rainbow Pattern (an improved 4th lvl version of Hypnotic Pattern), Shadow Magic (which allows an Illusionist to mimic Mage spells such as Fireball, Lightning Bolt, etc), Shadow Monsters/Demi-Shadow Monsters, Chaos (improved version of Confusion), Alter Reality and others simply aren't in the game anymore. And this last point is what hurts the Illusionist the most: he has to take spells that aren't thematic if he wants to be considered useful to the party. Instead of being able to chuck an illusory Fireball via Shadow Magic, anyone playing an Illusionist now has to take Fireball instead, which breaks the character concept. This is doubly true of anyone playing an Illusionist in Adventure League since there are no "Homebrew Rules" allowed in official play.

There is literally no reason for this problem. School of Illusion needs its spells back to give players the powers that now mostly reside with Evokers and Necromancers.....

Let me start this by saying: There are already too many spells. I'm not a fan of adding more that duplicate function just for the sake of having every school able to do everything.

Every Wizard starts out as a generalist at level 1, and Wizards are not meant to only learn a narrow subset of spells. There was never an intention that one's subclass should restrict their spell choices - this is one change you neglect from previous editions, where an Illusionist or other specialist was actually restricted from taking the spells from particular other schools. Instead, your choice of subclass lets you simply focus on a particular array of spells. Some schools don't even have spells at every spell level! In 5e, the only subclass that can get away with taking only within-school spells and still be generally useful is probably Transmutation, which also has one of the worst subclass feature sets.

Let's also flip your argument on its head and admit that Evokers are largely blasters and cannot contribute as well outside of combat as other specialist schools. Actually, Illusion is one of the few schools that performs well for all three 'pillars', given its useful defensive spells and very flexible (if creativity-requiring) spells like Major Image, not to mention very powerful control spells like Fear and Hypnotic Pattern. I agree that Shadow Magic would be a "nice to have", but it's also not as useful as previous editions because you already have no school restrictions for learning spells and you can already flexibly cast them from your list of spells prepared. If you want to talk about schools that need combat spells, let's consider Divination first...

I dunno. The fact you can make a permanent Major Image by upcasting it then use Malleable Illusions to keep around a permanent illusion that can be whatever you want - saving on spell slots - and can just make it real using Illusory Reality is pretty damn useful and effective.

Mirage Arcane with Illusory Reality and Malleable Illusions is basically granting you complete control over your surroundings.

Also, don't forget that 5e is not balanced mechanically the same way as previous editions. Levels, spellcasting, health, difficulty ratings, saving throws/resistances, and more all work differently, so some spells like the AoE Paralyze would simply not be balanced in 5E.