Takes all the work out of sight alignment and then you can focus on breathing, heartbeat and trigger squeeze.
I actually did once use a rifle with such sights to take some small game. It was not easy to aim outside of the conditions for which it was designed.
The military style peep + blade is a good compromise I think, especially when have to worry about ranging.
The hard part is having a solid hold and body control, reading the wind, and having super consistent ammunition that you intimately know all the elevation adjustments for. The remainder is how much money you spent on your barrel and how many rounds it has down it. A tight shooting coat helps a great deal, too.
I got bored with the whole thing when it occurred to me that I was just throwing money at barrels and other gear. Not to say that the game isn't highly competitive, but like auto racing, it's a money thing. Similar to many such pursuits, to take it to the max you will pretty much end up divorced.
And if you want to throw some money into the bow, you can put together the same bow that Olympic shooters are using for about $2000. The compound bows you see on the World Cup circuit are a bit more, perhaps $3000. Keep in mind that's for very top-end gear. (See [1] for examples of what I'm talking about.)
The rear peep sight on rifles take advantage of actual "optical effects", without any glass -- much like a pinhole camera can actually magnify images without any lenses or mirrors at all.
By simply providing an arbitrarily small "aperature" you're looking through in the rear, the front-rear sight alignment problem is not only capped at an upper bound of error (defined by the peephole size and sight radius), but the actual error from front-rear sight misalignment is visually magnified and centered through a fixed viewing point, making it vastly easier to keep the actual error near zero.
So generally, to achieve precision within the (small) upper bound of error with a peephole sight, all you need to do is place the front sight post on the target when looking through the rear peep sight. Even better precision is made much easier via a sort of "peephole camera" effect through the aperature of the rear sight.