It all comes down to how you miscomprehend a Cl-Alpha plot..
If your Alpha is at A, your Cl at B, due to your wing area, your weight, and airspeed, and you pop 60 degrees of flap,
Your Cl moves to C. Which is 4 degrees -past- your stall alpha.... well past it. Lots of lift... except the plane has departed long ago..
Since you can't change your wing area, or your weight, you have to change your alpha.. to the -same- Cl you had... after all, the weight, area and airspeed haven't changed... to D.. which corresponds to the alpha at E.. which happens to be 12 degrees -less- than that at A.
Unless you have a pivoting wing like a Crusader, you have to nose down... just to keep the -same- lift.
Your drag goes way up as a consequence of the flap deflection, and your Cm takes a walk towards instability.
But if you're one of those old timey round-motored planes, you come downhill nicely after adjusting alpha, without speeding up... even some kerosene stoves approach properly.. not wallowing around with their skinny noses in the air...