I'm not familiar with the terminology.
What is an "open" differential?
What is and what does the TCM do? Compensate the speedometer for a different gear ratio?
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Related to cost?
Recycler junk yards probably sell stuff based on scrap metal prices instead of MSRP.
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Is bigger diameter axles related to breakage?
What happened in 2014 that changed things?
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A very simple way (not very technical but to try and explain) open differential works by only spinning one tire at time, the tire that spins is always the tire with least resistance. a LSD (Limited Slip Differential) often called Posi or Trac Loc (depending on who makes it) Applies equal power using a clutch or other type of mechanism to make sure both tires spin
(Hence a two wheel burn out compared to a one wheel peel). Most Chargers are open differential with the exception of some higher end trims with the Getrag differential(such as SRT

. Open differential on our cars will still appear to make two wheel burnouts because the computer in the car will apply braking to the side of least resistance, hence making both tires spin, but it is not a true LSD.
A Transmission Control Module controls engagement and disengagement conditions for each gear and shift pattern along with other transmission related things. That's only the tip of the iceberg of what it does, but explains it in a nutshell.
I am not sure what happened in 2014 that changed things? Maybe it was partly the switch to the 8 speed transmission?
Hope that clears some things up, and is not too long of a winded reply.