What if the Janissaries never hindered the ottoman empires development?
The jannissaries were definitely a bad luck charm for the sultans, they effectively took people with a reason to hate them, gave them training, rose them up to fame and prestige, and made the their bodyguards. It was little wonder that so many of the sultans were deposed by their own bodyguards.
How did it impede the Ottoman Empire? Very little, in an empire as vast as that, the momentarily power struggle of a palace coups would not resonate very much. In fact, I doubt it would have very much effect on the lives of those working in the palace even.
I am sure that there would have been palace coups anyway, and that their existence neither extended or shortened the timeline of the Ottoman Empire significantly.
Janissaries were not the reason behind the Ottomans fall. They were the outcome.
Janissaries tried to rebel when they had chance. If the Padishah is not mighty and strong in his position, they did rebel.
When Sultan Mehmed II. came to Istanbul to take the throne, janissaries did the same. He paid some extras and dismissed the officers. After a while, he proved himself and janissaries couldn't dare again.
So, we can say that the reason behind the mutiny is authority gap but there were lots of reasons behind the fall.
It would be cruelty to throw all the blame on janissaries.
Janissaries did not hinder Ottomans' development. They didn't directly cause its development either (constituting Ottomans' mighty land forces and providing talented boys to ‘Enderun' school did help though).
When the Empire entered its decline period, line anything else, Janissaries also went corrupt and after a short while were abolished.
Summarizing a complex history of centuries in a couple of paragraphs is not suitable for an accurate account of what's happened and why. But all things considered, they had no direct political of economical effect on the rise and fall of the Empire.