The Allgemeine SS furnished the personnel for: the early Waffen SS units [that body guarded Hitler during the rise to power]. At that time SS units were under the SA command [Roehm], and were not allowed to exceed 10% of SA strength; the SD [SS Security Service], Himmler’s staff, the RuSHA [Race and Resettlement Office], and various other SS amter. They also were the umbrella organization within the SS for the “Honorary SS”- usually industrialists and party members. They were not just “scum from the streets”.
While the Waffen SS had their own command structure, they served under Army command [except for disciplinary purposes at the front. In 1940, Himmler put the Inspectorate for Concentration camps under the staff of the Waffen SS. He also began transferring troops between camp duty and the Waffen SS and back again, blurring the lines [Mengele was originally a medical officer with the 5th SS “Viking” division on the Eastern front].
The Einsatzgruppen were composed of German police units, SD personnel,and Waffen SS troops. On many occasions Army units assisted them [and participated] in Einsdatzgruppen actions. Of the four Einsatzgruppe commanders in 1941. Stahlecker, and Ohlendorf were SD [as was the CO of Einsatzgruppe ‘C’ [can’t remember his name]. The CO of Einsatzgruppe ‘B” was Artur Nebe, the commander of the Kriminal politzei of the Reich.
As for the Waffen SS, aside from their murder of enemy military prisoners [Wormhout, 1940 LSSAH; La Paradis, 1940 Totenkopf; Falaise Gap, 1944 HJ; Malmedy 1944 LSSAH, and too many incidents on the eastern front and in the Balkans to count]; there were the murders of civilians [Ouradur sur Glane, 1944 DR, Belgium, 1944 LSSAH].
The structure and interdependence of the SS is a little more complicated than your post indicates.
I quite agree, and note that the intention to blur chain of command and authority were very considered throughout the Nazi regime, as Hitler wanted no clear concentration of power under any one subordinate.