Just to clarify, are you asking why an army would allow people purchase commissions, or why someone would bother paying money for an officer's commission?
While previous questions don't address the precise points you are asking here is a previous archived question with answers including a link to a detailed study of the benefits both to the individual Officer and to the Crown of the British system
https://www.reddit.com/r/AskHistorians/comments/1hnrbx/what_were_the_effects_of_the_purchasable/
and another, similar question, here