Most people will be 360+ item level before they unlock the ability to gain +5 item levels on 340 Azerite pieces.

I'm behind the curve at 355 ilvl and HoA lvl 21, but I've been working on an alt that's at the same place. Still wearing ilvl 340 azerite that I can't upgrade to 345 for some reason even though I'm doing heroic raids/pvp and getting 360s/370s. Hell, I can't even use the defensive trait until 23.The highest heart of azeroth level in the world is currently 27 according to WoWprogress, which is what it takes to get a measly +5 item levels on a 340 piece. These people are generally above 370 ilvl already.