...arrows are easier to tune, better flight all around.
Add 'better accuracy' onto that and you've got the whole thing in a nutshell. Many of the old timers are astounded that shooting off the shelf is popular again because - many, many years ago - they proved beyond a shadow of doubt that shooting with an elevated rest is more accurate.
The deal is, the emphasis has been on instinctive shooting since the rebirth of traditional archery. (Emphasized almost to the point of foolishness, IMO.) Shooting off the shelf is supposed to be more conducive to instinctive shooting because it puts the arrow down close to the hand. Point the hand and the arrow follows.
Elevated rests are like 3-under release... If you use one, the purists have decided you must be using a gap system and, therefore, are not considered to be 'trad'. LOL
I've got a 1967 vintage Wing Presentation II recurve. Pre-compound, in other words, so it's gotta be trad. Right? Built-in flipper rest. NO SHELF at all. Shoots beautifully.
Then, going back the other way, the number one advantages to shooting off the shelf are simplicity, durability and dependability. The rest is permanently fixed in place. It ain't gonna move and it ain't gonna break unless the bow does. Pretty handy when hunting, especially in weather that's cold enough to cause a brass monkey to be concerned.