So in my mind I tied the crystal circuits into the crystal converter assembly into the (main) energiser to power the ship and warp engines.
So, what do the M/AM reactors do? What's powering the crystals? We also know the warp engines cannot operate without the crystals, and vice versa, the crystals cannot operate without the warp engines. In your model, the warp engines look like another ship system to power, so, loss of the warp engines shouldn't affect the crystal's power distribution to the ship; but we know this is not true.
I several cases, the warp engines (or better yet the M/AM reactors in the engines) are powering ship systems (via the lithium or dilithium crystal circuits). I think it more likely that the warp engines feed "power" from their M/AM reactors through the crystals for "usable" main ship power (energy?) with some sort of loop back to the warp engines. If the loop is a power dependence, then maybe main power from the crystals are providing power to the primary engine systems like the warp field generators and to the secondary engine systems like plasma injectors, heating elements, magnetic fields, cooling systems, matter collection, etc. Impulse and battery power systems cannot achieve the power threshold level necessary for warp field generators, etc.
In
MW, it is clearly stated that the engines pass power
through the crystals to power ship systems, and not powered only by the crystals:
FARRELL: He's had it, unless we put our deflector screen around him.
SCOTT: Captain, if we try, we'll overload our own engines. He's too far away.
KIRK: Cover him with our deflector screen, Mister Farrell. Scotty, Spock, stand by in the transporter room.
SCOTT: Aye, sir. (they leave)
FARRELL: We're protecting him, sir. We won't be able to hold it long.
SULU: We're overloading, Captain. Engine temperatures climbing.
CREWMAN [OC]: This is the Engine room. Temperatures are passing the danger line.
FARRELL Our deflector screen's weakening, sir. We can't protect them much longer. (lights flicker)
SULU: That was one of our lithium crystal circuits, sir.
[and later...]
SPOCK: The entire ship's power is feeding through one lithium crystal.
KIRK: Well, switch to by-pass circuits.
SCOTT: We burned them all out when we super-heated...
SPOCK: And that crystal won't hold up, not pulling all our power through it...
SCOTT: Our last crystal, sir. It's gone.
The above example shows that the engines were overloading to generate power for the deflector screen, and that power passed through the crystals damaging them. Even though the engines super-heated, they were still functional, but the crystal converter assembly took a beating with three crystals burned out and its last crystal with a hairline split at the base.
A similar situation occurred in
The Corbomite Maneuver where the engines were run well past their temperature limits, but the difference here was than the engines were directly providing thrust/propulsion. Here, the danger was blowing up the engines themselves, and not stressing or burning out lithium circuits by feeding power through them to other ship systems. Based on this analysis, the concept of a power dependence back to the warp engines doesn't hold up, or in this last case, the lithium crystals would have been popping like popcorn long before the engines would blow up due to overheating, and the overheating seemed much worse here than in
Mudd's Women. Another situation was in
That Which Survives where the engines were running wild. They were worried that the ship/engines were going to blow up, but no one seemed concerned about the dilithium crystals (or maybe the improved dilithium crystals don't burn out with engine overloading.) Of course, YMMV.
