That may be the rationale; I don't know. The only people I've ever seen try to leave the thrust lever behind are regional pilots; they usually come from a very regimented background and have a very narrow experience from which to draw, but I've yet to have an employer, training facility, agency, organization, etc, do that, from two-engine through four-engine.
Putting all thrust levers back in the hands of the pilot puts the feel and use of the the thrust levers back in a familiar, normal environment; (s)he is used to having all levers in hand, and an emergency is not the best time to alter that. As noted, controls or switches such as a go-around switch may play a factor. When more than two engines are involved, the tactile sense of matching thrust levers is one to another, or for those aircraft that may have split thrust levers (because the thrust doesn't advance evenly, mostly older aircraft), keeping the same relative position is nearly impossible during power changes, especially large ones, if all the thrust levers aren't in hand. A missing thrust lever might make it easier or possible to push up the wrong one at the wrong time, or retard the wrong one at the wrong time. On aircraft that lack a limiting function (such as FADEC), because turbine engine top ends can't be trimmed when setting up the engine mechanically, it's very possible to overtemp or overboost by pushing the power too far on one or more engines; with an engine-out or loss of an engine's instrumentation, having all the levers together serves as a common reference for all, creates a full picture in the hand (instead of say, a gap in the middle between levers, etc), and a reference for more even, familiar use of thrust.
The initial step of retarding that lever is meant to only identify the failed or malfunctioning powerplant, while reducing or eliminating fire/overheat, bleed leak, overspeed, vibration, etc. Once the decision has been made to cage that engine and it's been fuel chopped, or even feathered and secured (such as holding the lever behind the gate on certain garret-powered airplanes, while the prop spins down, to keep it on the locks), the thrust lever aft has no further use. There are a few installations out there where, in certain malfunctions, pushing a thrust lever forward on a dead engine that didn't feather, may be the only means of reducing drag, which may be critical on a go-around or at a time when all available thrust is needed. That won't happen if the thrust lever is back.
If the crew never bothers to secure the engine at all, that's another matter, which appears to be the case in the mishap at hand. The crew retarded the lever on the good engine, operated the bad, and did nothing proactive until impact. While not a lot of time existed, they had two thousand feet at one point, and shortly there after, none. The event, however, began at less than 400', when a turn procedure would have been appropriate, followed by a climb to an initial cleanup altitude, followed by a procedure for identifying and caging that engine. So, failure to take action.
Failure to cage the engine, or properly secure and shut it down, doesn't stand out to me as the most glaring problem in the narrative, however. Shutting down that engine wouldn't have reduced drag or improved their state much, if at all, from a practical perspective. The larger problem was the implicit trust the captain described; an infallible first officer, no desire, effort, or reason to check the engine instrumentation himself (because the f/o "never makes mistakes," and "always makes the right call"). There should be a declaration of the problem, which was vague at best in the case at hand. Looks like number one. We lost number one? Yeah. Not helpful, open to interpretation, requires questioning, and the initial call could go either way. Looks like number one (is the good one?) (has failed?). I've yet to see a training program that didn't require a declaration of the problem: we have an engine fire on number 1, oil pressure loss on number one, number one fell off the airplane, there's a little green man with a leatherman tool tearing the cowling off of number one and a bad method actor seated directly adjacent to it, etc.
Standard conventions, such as returning the thrust lever to the control of the pilot flying, serve a valid purpose, but so do conventions such as declaration of the problem, formally calling for the correct QRH procedure, and so on, to say nothing of completing a procedure, or doing any procedure at all. The implication of the narrative here is that the crew did practically nothing until impact, which makes their survival all the more miraculous. It's interesting that the captain so doggedly clung to his beliefs and personal narrative that he became combative with the investigator interviewing him. It further reinforces a false belief that appears, based on his own wording, to have led him on a course of inaction, and to idle a useable (I hesitate to say "perfectly good" when referencing this employer) engine at a time when it would have saved the day. This is the nightmare of all pilots who pray Lord, please don't let me screw up, now to have that very screw-up on display.