base stats of early game vs. late game champions are not very distinguished.
That makes the game much easier to understand and more user-friendly.
Base stats being a solid base rather than some wild crazy ride is a good thing, as giving crazy variations runs into a ton of design issues.
The biggest issue with differing base stats is you make all flat bonuses mean substantially different things. a 10 AD bonus in an item or a 10 AD bonus on a steroid change in value substantially based on context if some champions start with 30 AD and others with 80.
With base stats being largely the same: it allows a 10AD bonus in items, masteries, runes, or abilities to mean largely the same thing accross all champions, where 10 AD equals 10 AD.
It also allows abilities and how abilities interact to tell the whole story of how a champion works. With base stats being really similar, you don't have to worry about a 10 AD steroid actually costing you 10 AD from your base stats, costing a skill point just to put you even with your opponents. Finding out skills opperate as such is extreemly annoying.
Also - with defining champions through base stats you run into substantial item-scaling issues.
If you set up a tank to have 1000 HP and only do 50 damage per AA where you set up an Assassin to have 500 HP and do 100 damage per AA, they're both balanced. It takes the tank 10 hits to kill the assassin and the assassin 10 hits to kill the tank in a straight-up slugfest.
However: When you introduce a +500 HP item and +50 AD item things get awkward.
On a tank, the +500 HP item only increases their 1000 HP to 1500, a 50% boost: or a 50% boost in overall power. However, the +50 AD item doubles their strength: boosting their 50 AD hit to a 100 AD hit, a 100% increase.
The inverse issue arises on the DPS champion.
So with HP item vs. HP item: the glass-cannon wins:
1500 HP 50 AD vs. 1000 HP 100 AD
- tank kills in 20 hits, assassin in 15.
With AD item vs. AD item: the tank wins:
1000 HP 100 AD vs. 500 HP 150 AD
- tank kills in 5 hits, assassin in 6.67
TLDR:
Base stats being the same prevents confusion. You read a champion's kit, you know what they do. You don't have to worry about spreadsheets with their stats compared to everyone else.
Consistent bases also prevent pushing a champion into their opposite intended roll due to how flat bonuses scale.
or another 2 defensive item build rather than all offensive items + GA.
