So, so far the mechanical implications of Large size might include:
Large
+ can access larger weapons with higher damage
+ an aura, such as from a spell, can affect more adjacent targets
− can be attacked by more adjacent hostiles
− can incur opportunity attacks from more adjacent hostiles
+ can block wider access points
− might need to squeeze thru more access points
+ increases carrying capacity
+ can as a ‘mount’ for an ally
‘At the end of the day’, dealing more weapon damage seems to be the only notable concern.
The problem of blocking access points seems trivial to fix. Repurpose the grappling mechanic to squeeze past someone.
Affecting more adjacent creatures seems offset by being affected by more adjacent creatures.
What D&D needs is a balanced mechanic that can normalize larger weapon damage.
In other contexts, I want size to correlate with Constitution, so each size has a minimum requirement. Something like:
Minimum Constitution Score for Size
27 Gargantuan
23 Huge
19 Large
15 Heavyweight (Medium)
11 Lightweight (Medium)
7 Small
3 Tiny
Thus the larger creature only deals more damage by adding the Constitution score to the damage. (Better yet, Strength is only the attack bonus, while Constitution in the sense of size becomes the damage bonus.)
So, players who want to deal more damage by being Large need to invest in a higher ability score. This is an opportunity cost that results in other ability scores being lower. Thus, a more balanced Large character is possible.