I do understand that its not usually a "prioritary rush" but in case you go for a early luch build relying on sturmpioniers medpacks to heal the heavily wounded units and you see the enemy harfblobbing you can easily stop thinking on the luch and get the stuka on early game.
Still, going for med hq you can get flak ht, if you spot for him it does a great job way earlier than the stuka (stoping, but not killing ofc)
Again. What you're suggesting is not really early game.
The problem is that OKW neither has good support weapons to control mass enemy infantry (Can't counter support weapon spam effectively either. See: maxims) nor good abilities to punish blobbing early game. Scavenge doctrine being the closest to fulfilling that role.
This all leads to OKW being a shitty one dimensional faction (not necessarily underpowered). Having to either blob harder than whatever it's playing against or locking your fuel and hoping that the enemy isn't good enough to push you into your base until you get better tech.