Pre-declared spellcasting resolves this: Everyone knows that the wizard is casting Fireball at point X. The character who beat the wizard's initiative notices this in time to move clear of the blast zone. The character whose initiative is worse than the wizard's reacts too slowly and gets fried.
How does this logic even work?
Both PC warriors are charging into a melee. No one in the PC's side would be able to know that an enemy spellcaster is casting a spell, or when or where.
Both soldiers are rushing an enemy position. No one on their side would be able to know that an enemy is preparing to throw a grenade, or when or where.
See how ridiculous that is? If the enemy is taking physical actions to prepare an upcoming attack, you can see and respond to that, regardless of whether the actions are wild gesturing to cast a spell or the relatively more subdued act of pulling the pin on a grenade. And we know from real-world data that people can sometimes (but not always) react to incoming grenades before they go off, so arguing that they can't have a similar possibility of reacting to spells being cast at them seems a bit off, unless you're interpreting spells as being cast instantaneously, rather than requiring some seconds of gestures and incantations before the spell takes effect (as the fluff of most RPGs says they require, even when the rules treat them as being instantaneous).
Even if they notice the wizard is casting something that still requires a Spellcraft (or is it called Arcana now?) check to even know what spell they're casting.
This part beats the hell out of me. I haven't played D&D on the regular in decades, so I have no idea what their current rules on identifying spells look like.
And the PC with the highest Initiative notices the wizard but the other doesn't? When did an Initiative roll become a Perception check?
There's a lot more to situational awareness than just perception. One fighter might notice the guy in robes gesturing wildly (or one soldier might notice the guy grabbing a grenade and pulling out the pin) while the guy standing next to him is too focused on something else, even if the second guy is more perceptive and keenly aware of every tiny detail of the thing he's focused on.
And how was he able to strike at someone in the melee if he's now avoiding the spell's blast radius covering that same area? How did the other one get there first if he hasn't had time to act that round?
I have no idea where you got this order of events, where one guy runs into the blast radius, takes a swing, and runs back out, while the second guy stands outside the blast radius doing nothing at all, and then the second guy gets hit.
Let me spell it out for you, step-by-step:
1) Wizard declares that he's casting a fireball at the space where two opposing fighters are currently standing and begins the process of casting it.
2) Everyone rolls initiative. Fighter 1 gets initiative 76. The wizard gets initiative 67. Fighter 2 gets initiative 18.
3) On initiative 76, fighter 1, seeing that the wizard is in the process of casting a fireball in his direction, moves out of the blast radius.
4) On initiative 67, the wizard finishes casting his fireball. Fighter 1 is not affected because he is no longer in the blast radius. Fighter 2
is affected because he has not yet reacted to the spell being cast.
5) On initiative 18, fighter 2 does whatever, assuming he's still up and fighting.
Note that fighter 1 does not get any extra actions as you seem to have presumed ("how was he able to strike at someone in the melee if he's now avoiding the spell's blast radius covering that same area?").
None of this really addresses the actual scenario. It's just jumping through hoops to justify initiative and favor characters with high initiative rolls by giving them extra abilities, like evading area effects that took effect after they were already supposed to have moved into the blast area, or interrupting casters who aren't even within melee range.
He's not "evading area effects that took effect after they were already supposed to have moved into the blast area", he moved out of the blast area
while the spell was still being cast,
before it took effect (because the casting was not yet complete). In the modern-day equivalent, he moved out of the blast area while the opponent was pulling the pin on his grenade and throwing it, not after it had already exploded.
You seem to be viewing all actions as happening instantaneously when they are declared, and my point is that some actions take time (casting a spell, or pulling the pin on a grenade, throwing it, and waiting for the fuse to run out before it goes off), which allows people to react to - or, yes, potentially interrupt - the lead-up to the final event before it happens, whether that reaction is to leave the fireball's blast radius, or trying to pick up a grenade and throw it back before it goes off.