Consider airline ops where the only visual approaches they do are in the simulator. One would argue that that conducting an instrument approach is the safer option. You only have to watch visual approaches flown by heavies into say Kansai onto runway 24 for about 30min to realise how little practice these guys get. As mentioned above, obstacle or terrain clearance calculated for you with a vertical profile or electronic slope guidance is safer than a visual approach. Remember some of these longhaulers do less than half a dozen landings a month.
Not sure that there would be any great fuel advantage in flying a visual approach vs runway aligned instrument approach. Also, atc/traffic delays dont allow you the flexibility to just do what you want.
Maybe the benefit you are refering to is for non precision non runway aligned approaches OCTA in VMC by IF pilots who arent training or updating their recency, or being checked, or improving their proficiency, or approaching an unfamiliar runway or flying a straight in approach... There are a few reasons why we do it. Hope this helps.