All my biz cards have been SP approvals actually. I've had 3 total HPs for 8 AMEX cards. My first ever (Hilton, which I have since closed), my second (SPG Personal, opened in Sept. 2016), and my Ameriprise Plat (opened Apr. 2017). The rest of the approvals had no HP.
I've opened 3 new Amex Business cards since July and all have been Softpulls.
Biz Delta Gold
As others have stated, I cannot comment to the maxed out part, I was carrying a balance on my Plus (65% util) when I was instantly approved for the Business Delta Gold.