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I don't really believe that it's not like they were the only Muslims or that Christians could not be that way either plus the Ottomans still relied heavily on Christians, not just the Janissaries that were converted but also those that kept the religion such as in the Balkans.
They did try to modernise and brought in some French Reformers to do it who did have a bit of success. The problem with that is that it's institutional, it's the same reason why China could not modernise. It's not that hard to make a musket, it's not that hard to make a cannon and it's not that hard to teach basic drill in both. What the Ottomans and Chinese lacked were dedicated institution of professionals whose jobs it was to research and develop new tactics and equipment and then institutions that would pass this on to the army and hold the army up to a standard where it can use them. Sure, they had individuals that would dabble in it and they of course had training schools but there just wasn't the drive or professionalism that the west had, the French would come in, teach them some things, set up some factories and then it would all fade away in a few years.