What are the benefits of on-chain transactions?

Could you elaborate on the advantages of on-chain transactions in the world of cryptocurrency? As a professional in this field, I'm curious to understand how they offer benefits compared to traditional off-chain methods. Specifically, how do they enhance transparency, reduce fraud risks, and enable faster and more secure transactions? Additionally, are there any cost-saving benefits associated with on-chain transactions? Your insights would be greatly appreciated in understanding the full scope of their advantages.