The Ministry of Magic is essentially a thugocracy where all the thugs wear nice robes and fancy suits. Ministry personnel have rather broad powers to snatch and to search and to imprison and even to politically assassinate with not only a carte blanche but with a blind eye turned. They also mistreat Muggles with reckless abandon -- "fixing" their memories and "wiping" their memories, always without any knowledge and always without any kind of consent of the altered person -- all of which constitute extreme examples of torture & manipulation. The Wizarding World has no concept of the dignity of the human person, especially when it comes to Muggles. But their concept of humanity is little better when it comes to magical peoples of various sorts.
Some of this may stem from how police powers and the justice system work in the UK, of which I plead ignorance. While, ostensibly, the MoM is some kind of hidden branch of Her Majesty's Government -- we know a new Minister of Magic pays at least one courtesy call on the PM at his taking on the office (and presumably the PM can, via the Portrait in his office in No. 10, communicate with the MM) -- it is a branch with little or no oversight and run by corrupt officials with little to no concept of due process and, frankly, an unsurprisingly medieval understanding of justice. (For example, it apparently wasn't too awful long ago that punishments at Hogwarts involved torture, according to Mr Filtch's fond reminiscence.)
At the best of times, the MoM is an invasive and oppressive presence within the magical community in the way it arranges the lives of its citizens, from the Trace to all but forcing families to funnel their children through a narrow and officially watched progression of life, be it wand registration to the Trace to blood status registration, wand confiscation, examination, and even destruction.
The WW's justice system is really just a symptom of an extremely corrupt Ministry operating in a rather top heavy, self serving, and almost fascist bureaucracy. The very fact that dementors are present for hearings and trials is the functional equivalent of placing a Muggle defendant in a noose whilst on trial. Everything about the MoM's justice system is designed to frighten, demoralise, terrorise, and oppress everyone who sits on the wrong side the "law". Note also that there is no jury, no proper recourse to legal counsel, no actual trial procedure and no actual judges.
In conclusion, may it please the court! In the Wizarding World, people are sent to Azkaban before trial, simply because the system of jurisprudence in the Wizarding World is barbaric, antiquated, medieval (in the worst sense of the word) and completely out of step with a more modern and enlightened understanding of mercy in justice, human rights, civil rights, and the rights of the accused. They do it because they can, and no magical people seem to really care or be aware of the barbarity of their government; let along care enough to desire to change it.
As an aside, I don't think we can really blame the average witch or wizard on the street for this attitude. As a culture, British Wizarding society is terribly backward and parochial in general. Not just the blood status thing, but the absolutely blasé attitude even those on the side of the Light exhibit towards other human beings, be they Wizards or Muggles, and to say nothing of their absolutely uncaring and unconcerned attitudes towards Goblins, Elves, Centaurs, and any other magical peoples. Basically, wizarding society is about as phoqued up as North Korean society. It took a Muggle born (Hermione Granger) to even make her age group aware there is even an issue to be aware of!