The example you give is a very interesting case, but irrelevant to the actual American justice system as it is an example of military court which utilizes a different, more fast tracked system of fact finding, testimony, and punishment. Further, it is an anomaly within the military court system as America since the Civil War has been very reticent to punish desertion with death.

However there is something to be said about the length of time between sentencing and execution in America's standard justice system. There are many examples in the modern world of the worst criminals dying on death row of old age or natural causes because their executions are stayed almost indefinitely. This is the result of several court cases and cultural icons beginning in the mid 1920's with the execution of Sacco & Vanzetti, two anarchists fast tracked to die with flimsy evidence of their guilt and a massive public movement of support behind them. The amount of petitioning and protesting done by the public lead to massive reforms within the State of Massachusetts justice system including the set up of an independent review agency for death penalty cases, which has been adopted in other states as well.

Roughly 30 years later, similar public support was put behind a prisoner named Caryl Chessman, being put to death in California over a string of non-homicidal kidnappings. He published multiple books while awaiting death, explaining the conundrum of being put to death for a crime spree that never killed anybody. With his writings the public began a campaign to stop executions for kidnappings under the Lindbergh Law, and abolish the death penalty entirely.

The death penalty was abolished for a time, with the passage in the Supreme Court of Furman V. Georgia (1972), which caused all existing death sentences to be commuted to life in prison (yes, this included Charles Manson), but after a petition 4 years later the case Gregg V. Georgia (1976), the death penalty was tentatively reinstated, with extensive legal constraints that make the due process on it a years or decades long affair. A great number of states have chosen to get rid of their Capital Punishment entirely, and even in states that still have Capital Punishment, there are governors who have declared moratorium on executions, thus making it a rather expensive alternative to life in prison.

That's a military court, not a criminal court. There was probably an ad-hoc tribunal set up to try him for desertion. Since it was during wartime, and a particularly demanding and difficult period of wartime, they didn't dawdle. They also wanted to set an example.

The rules are different for military trials than for civilian criminal trials.