This is a really interesting aspect of MOBA design and philosphy.
I would say yes this is intended by design, but indirectly.
We don't design the map/roles so that someone is under-leveled, no.
MOBA design includes a lot of pillars: Mechanical Skill, Strategy/Tactics, Flexibility, and Resource Management to name a few
The resource management is what most relates to this topic (and character flexibility but less so) and in mobas those resources are shared. The total XP/Gold on the map is a fixed amount, and its up to players to decide how to share it, or how to take it from their opponents.
Support being under-leved is actually a META result of that core design philosophy.
Players have discovered over years of competition and testing across multiple MOBAs that its a factual winning strategy to have someone sacrifice their access to resources to empower their team as a whole.