I would imagine that it would be considered more humane, but considering how it would probably even more humane to just make them forced laborers, I don’t understand the reasoning. Also the Nazis went out of their way to suppress evidence, so why did the level of mercy matter? Was gas more expensive than firearms or physical force?
The main reason was the effect on the executioners.
Von dem Bach-Zelewsky in one of his postwar statements described at length how Himmler witnessed an execution of Jews by shooting and was convinced that it had a negative effect on the shooters. A better method had to be found, and gas was experimented with for the mass murder and found acceptable. (Though it should be noted that by that time gas had already been used to kill the "euthanasia" victims, first gassing took place in 1939.)
You can read the excerpt here (scroll down to the images of the 4 pages): http://holocaustcontroversies.blogspot.com/2017/01/on-mattognos-hallucination-that-von-dem.html
That said, even in this excerpt they were mentioning how the new method they found was more humane. The pretense of trying to kill their victims more humanely thus did exist, whether or not the Nazis themselves believed in this.
This notion appears in several documents about the gas chambers.
Thus in the 1942 letter of Becker to Rauff about the problems with the gas vans we read:
http://holocaustcontroversies.blogspot.de/2015/10/contemporary-german-documents-on.html#_doc9
"The application of the gas is not undertaken correctly. In order to come to an end as fast as possible, the driver presses the accelerator to the fullest extent. By doing that the persons to be executed suffer death from suffocation and not death by dozing off as was planned. My directions have now proved that by correct adjustment of the levers death comes faster and the prisoners fall asleep peacefully. Distorted faces and excretions, such as could be seen before, are no longer noticed."
The last sentence indicates that the worry was, again, more about the executioners.
In a 1942 script for a propagandistic euthanasia film we read:
"The incoming gas is completely odourless and initially robs the patient of their powers of judgement, and then their consciousness. Completely unknown by the patient, without pain and without struggle, the deliverance of death takes effect."
The propaganda nature of the movie made such a mention a must, of course.
Finally, in the 1943 report by Franke-Gricksch about the mass extermination of Jews in Auschwitz we see every similar language:
http://holocaustcontroversies.blogspot.com/2019/08/nazi-document-on-mass-extermination-of.html
"When the containers reach the floor of the pillars, they produce certain substances that put the people to sleep in one minute."
This was sort of an internal propaganda (as the analysis of the rest of the report shows) since of course the victims didn't die in one minute and had to suffer, but Franke-Gricksch wanted to create a picture of a peaceful death.
The notion that it would be more humane to make them forced laborers doesn't make sense. Because as a rule (with some exceptions, like most Soviet Jews, considered especially dangerous) they were gassing the Jews unfit for work, while selecting those able to work for the work camps. You can't make slave laborer out of someone unfit for work.
If you gas e.g. 2000 people in a stationary gas chamber, you only need the guards to push them in, and one or two people to introduce gas (in Auschwitz - one or several Zyklon B cans; in the Aktion Reinhardt the exhaust gases of gasoline engines were used; in both cases the costs per victim were laughably cheap). The body disposal was left to the Jewish special teams.
If you're shooting 2000 people, you need at least as many bullets, and a considerable shooting team (that will be traumatized to boot), as well as lots and lots of time.
If you're using gas vans, you can kill maybe 50-80 people at a time pro van, so here the efficiency plays a secondary role, but the stress on the executioners is significantly lower.
I think it is quite obvious that mass gassing in stationary gas chambers is by far the most efficient industrial mass murder method.
Which is not to say that the mass shootings stopped with the introduction of the gas chambers; sometimes it was simply more expedient to shoot people locally. There were up to 2m shootings of Jews by various mobile units (not only Einsatzgruppen), so their number is comparable to the number of the gassed Jews (ballpark 2,5m). So although the gassing was numerically preferred, it was not by that much. And when we take the shot non-Jews into account it may be a wash.
As stated by @Sergey_Romanov, the primary reasons were efficiency and effect upon the murderers. Testimony of sonderkommando, Jewish prisoners forced to work in the crematoria, describe the deaths by gas as extraordinarily brutal. Filip Muller, a sonderkommando in Auschwitz described people tearing their fingers off while trying to escape, vomiting, defecating, and frothing at the mouth, tearing at the bodies of other people, children crushed under the weight of the bodies above them, people were bloodied from beatings on the way to the gas chambers. Muller even testified to women giving birth as they died. People fought like hell, trying to get out, or get to the top of the pile of dying people so as not to be crushed, it was certainly as brutal as the mass shootings carried out previously.
http://www.auschwitz.dk/Docs/new_page_11.htm
Inside the Gas Chamber by Shlomo Venezia
Eyewitness Auschwitz by Filip Muller