Can a code word be assigned to a DSC-TR session and then the client given permission to use the code word to replicate the session over and over? Would that work, and if not, why not?

This would have a small benefit contributed by the general desire and intention for something good to happen, but the client personally could not substitute for the practitioner’s intentions tied to the code word. There would be a dilution effect in being once removed like this. This is why having an act of magic that is simple to transfer to others is but a dream. Telling people to say "Abracadabra" when they want something will not be effective in getting something done. What you propose is somewhere in between. It is analogous to a prayer request that is of a general nature because the specificity being tied to that code word originates with the practitioners and ironically not with the client even though they are the subject of attention for the session that was carried out. So this is a useful idea and has a benefit, it would not be the equivalent of having the practitioner re-launch the session using the code word. The benefit of what you are proposing is thus real but would be modest.