We unlock the last battleground that rewards a weekly pinnacle or something.

How much higher do pinnacles drop?

The level of the pinnacle drops you're getting is a +1 or a +2 above your “average”. So, it is quite possible you can get the same number (or lower) than the highest piece you already have.

How long is battlegrounds Destiny 2?

Complete three Battlegrounds activities from the playlist

Doing so will earn you tier-two Powerful Gear, and considering Battlegrounds only take about 15 to 20 minutes, that's a great deal.