This question is a very much like asking why it was Stan Lee thought adding The Hulk to his new Avengers series made sense...
The truth is when the Justice Society were brought together in a book back in 1940 writers didn't make any distinction between vigilante's, Super-Heroes, or supernatural characters. There were no lines separating these three, very distinct, areas. In 1940 The Spectre was a character regarded as being a being a Ghost, a Ghost with amazing powers sent back to earth to punish evildoers, that he dealt with criminals in gruesome ways was merely what he did, no one made the distinction that this method and approach was unacceptable as these were evil people and evil people deserved what they got. Bear in mind that in his initial appearances Superman was both willing and capable of breaking the law to achieve an end and would treat crooks in a manner that would be really rather unacceptable by todays standard. The Batman too was a vigilante who used whatever methods he had to, occasionally carrying a gun initially he would quickly be given Dick Grayson to tone down his darker nature and by that same time Superman was refining his better nature to.
How society saw law and punishment in those days was a good deal more black & White than what we are accustomed to, and if there was a turning point then it may well have come with 1966's Miranda Report, which was an act of US government that brought in clear guidelines for police and law enforcement that granted greater rights to suspects and the just arrested giving them some protection from being unduly judged before any actual legal process or trial had assessed their guilt or innocence either way.
In 1940 the Justice Society was the first of its kind - a gathering of "Mystery Men" to form one crime-fighting team that would take on the challenges and threats that no one man could deal with.
The Spectre was seen as being little different to Doctor Fate, The Sandman, or The Green Lantern; like them he was just another exotically costumed character with amazing powers and a spooky air. How he would develop in the years after 1940, and how society slowly changed its levels of acceptance, dictated how long he would stay with the JSA and what their own eventual attitudes towards the other. Suffice to say It gradually became apparent that The Spectre wasn't a logical fit with the group and with his reintroduction in the Silver-Age, and truly godlike powers and aspect, his status was cemented. No more super-teams for him.
Is the Spectre now even viewed as being the most powerful Superhero, or is he seen as something else?
And did the Phantom Stranger take his role on the JLA than?