No.

If all girls can meet each other in the same space, then it is harem.If he alone can maintain stable meeting without each girls from different world ever meeting each other properly in the same space, then it is not harem.

personally, I do not like his claim that quirkless can fight back, since his power come from a system. This will also cause other quirkless to be capture and experiment.

I'm okay with time skip, but please consider this. Since Izuku now know about his impression on other, have him learn a type of aura/acting/hot cold reading skill to gain good faith. Cat/bird taming skill works too. While on the same time, search for dungeon at the surrounding. Will there be party system? or tame pet allow to move out from/ into the dungeon?

it might be better to get observer as 3rd class, since it will help it identify hint before, during & after event happen, & normal everyday interaction with allies and neutral party. The idea of no 1st defence in avenger pretty scary since we can't be sure what attack the enemy will use.

berserker. i believe most enemy he face will not be normal size humanoid, martial art type of guy, and AOE. berserker can help boost his status in long battle. plus the guardian can help manage his health and stability.

A good story, waiting for the next update. Will MC use clones on every civilian for faster leveling?