The peculiar method of Ottoman succession was detrimental to Ottoman power because each son would gather supporters to support them throughout their provincial governorships, and this in turn meant that when the Sultan passed away, the sons would rally the people, and use them against each other, cause revolts and strikes, making the country chaotic. The consequences were even worse when one of the sons started killing their brothers/half-brothers in order to claim the throne as quickly as they could as it would cause more discontent between the people. Although the revolts did clear up by the time the new Sultan had come to place and settled the country, this ultimately led to the decline of the Empire as the social state of the country was unstable. Since the people themselves had the power to make a change to the country, this peculiar method of succession caused the decline of the Ottoman Empire because it, in turn caused instability amongst the people, which proves that it was the underlying factor.
However, this is not entirely true as since the Sultan had absolute power and was able to control the people, the people had to maintain the peace within the society or face his punishments, which were usually harsh, in order to discourage people from disobeying again in the future. And since the Sultan, who was supposedly the most fit for the job amongst his brothers, had the ability to control the people, it is a given that he is able to do his job well, or better compared to his brothers, who were less competent. Thus rather than lead to the decline of the Ottoman Empire, it should actually bring the Empire to greater heights.
However, this was ultimately untrue as because of the rivalry between the sons of the Sultan, killing eventually became replaced with keeping all the sons in the Harem in order to prevent them from harming one another. Only when the Sultan passed away were the sons allowed to leave, and usually the eldest son would become the next Sultan. Staying in the Harem meant that the sons were not allowed to gather any support from the people as they were not allowed provincial governorships anymore. And since staying in the Harem for such a long time was detrimental to their mental wellbeing as future leaders, the eldest son was no longer the fittest to be the Sultan, let alone the other sons. This robbed them of their chance to become Sultan, unlike the earlier, more “meritocratic” system.
Therefore, the peculiar method of succession was detrimental to Ottoman power as it ultimately backfired.