Yes, you have correctly interpreted my first sentence. I could have added a clarifying phrase at the end, "so don't do that", but you got my point. The downside to avoiding mixed u-P element formulations is in models with highly incompressible materials where Poison's ratio is almost 0.5 or where hyperelastic materials are being used. Some of these models will not converge without the mixed u-P element formulation.
Looking at the table of elements, it answers your question of why you have 1 million solid or shell elements and an additional 3 million other elements. Oh, and in my example with SOLSH190 above, where I got to 5x more elements, I could get to 9x more elements if each of the contacts were set to symmetric where ANSYS duplicates the contact but reverses the sides for Target and Contact.
I don't fully understand the "entangles" phrase, but it could mean the case where you have one set of contact elements or a joint on one face and another set of contact elements or a joint on another face and they share a set of nodes on the common edge. You often see warnings about that.
This part of the ANSYS Help system tells you how to avoid using Largrange Multipliers in MPC184 elements.