I agree with you actually. I'd like to know what the original idea behind standardised MR was, because it seems kinda... useless to me.
Most likely scenario is it's a carry-over from DotA.
In Warcraft III/DotA , all Heros have Hero armor. Hero armor reduces spell damage by 30%.
Another thing to note with base stats is there values are pretty basic and almost identical across a wide range of champions.
This actually does a lot of good things in regards to clarity and item balance, because figuring out what 50 AD is worth is pretty easy if everyone has ~50 AD at level 1 and ~110 AD at level 18.
All a player needs to do is check a champion's abilities and see if AD has good interactions there, they don't have to pull up charts to cross-reference a bunch of champions and their abilities because that cool skill with good-AD scaling was meet with an AD scaling 'tax' on a champion's base stats that makes them put AD to worse use than an average champion.
Skewing base-stats also pushes counter-intuitive item builds in several situations.
Say you have 3 champions with widely variable base stats:
1000 HP 100 AD, average.
2000 HP 50 AD, tank.
500 HP 200 AD, glass-cannon
All 3 of these are balanced against one-another, as they take the same amount of time to kill eachother. The average champion needs 20 hits on the tank and needs to be hit 20 times by the tank, the average champion needs 5 hits on the glass-cannon and needs to be hit 5 times by the glass-cannon, the tank and glass-cannon need to hit one another 10 times to kill each other.
However: things go wrong pretty fast when adding a 1000 HP and 100 AD item into the mix.
The glass-cannon will be able to triple their HP with the 1000 HP item, going from 500 to 1500, where the 100 AD item will only see a 50% boost in their overall power, 200 to 300.
The tank will inversly see a massive power-spike with offense, as grabbing the 100 AD item will boost their 50 AD to 150, where grabbing the 1000 HP tank item will only see a 50% boost in HP from 2000 to 3000.
If the glass-cannon grabs the DPS item vs. the average champion grabbing the DPS item: it's 300 AD/500 HP vs. 200 AD/1000 HP: requiring the average champion 3 hits to kill the glass-cannon but the glass-cannon 4 hits to kill the average champion, making the glass-cannon below average.
If the glass-cannon and average champion grab the tank item, then it's 200 AD/1500 HP vs. 100 AD/2000 HP. In this case the 'glass cannon' needs to strike the average champion 10 times to kill, where the average champion needs to hit the glass-cannon 15 times.
Item scaling in LoL is all kinds of awkward.
But this interaction is also fairly present in a wide range of champion kits.
Nasus gets a ton of damage for free without getting much in the way of free tank stats, causing Nasus to itemize like the glass-cannon above. He innately does so much damage there isn't much point in building more damage on him, but he's also pretty fragile innately so building defense on him makes a ton of sense.
On the other hand: Kayle can turn invulnerable, and taking 0 damage is pretty hard to beat when it comes to tanking damage. With her decent range, speed, and CC all adding more layers of protection: Kayle has a ton of innate defenses to merit pursuing heavy damage.
Sorry about the post length.
But those are the main reasons for fairly static, or actually static base stats.
Messing with bases can push champions in the opposite direction of that change's intentions, changing bases can make a champion's optimal interaction with itemization extremely muddled: making stats feel widely inconsistent and difficult to compare between champions, and differences in champion play-styles and itemization interactions can be set pretty efficiently through abilities alone.