This topic can be as divisive as whether training deadlifts with straps is effective or not. Since powerlifting is my background, and powerlifters tend to be the biggest proponents of the false grip (AKA suicide grip), I'll attack the question from that perspective.
- Have no reason to use a false grip on bench press. There's too much they need to get right to add unnecessary risk.
- A beginner is using such light weights that if they do end up letting the bar roll, the thumbs around grip will be good enough to help them catch themselves.
- For sources, check out "Starting Strength", and I believe venerable Mr. Wendler with 5/3/1 also suggests that beginners use a thumbs around grip.
- Any overhead press doesn't have the same risk involved as a bench press
- If the bar rolls out of the hand you drop the bar and have the opportunity to get out of the way
- Wendler absolutely advocates a thumbless grip for overhead press in his 5/3/1 book.
- Paul Carter advocates it for overhead work as well.
- I've found it to be less stressful on my wrists
- As you progress your technique enough, you can consider using the false grip.
- I've found it really depends on how wide your grip is as to which grip feels better. The wider the grip the more false grip feels better. The narrower the grip, the more thumbs around feels better.
- Paul Carter uses thumbless grip, but recognizes that it's a very individual choice.
- Most powerlifters I follow take more of a laid back attitude along the lines of "if you have everything in order and it feels better, use the false grip".
I've seen arguments on both sides, but the general consensus seems to be it's not something beginners should do because of their inexperience.
Bench Press Safety
The biggest detractors of the false grip site safety as the number one reason why not to use it. The problem is, the bench press accidents I've personally witnessed and ones I've read about wouldn't have turned out any other way if they used a thumbs around grip.
In a power lifting competition, it is quite common to have 3 spotters. One on each end and one in the middle. The problem is that the reaction time for anyone is so small, chances are the bar is going to hit you. When the bar has 350+ lbs loaded on it, the bar is going to continue falling even though the spotters are doing their best until they can overcome the inertia of the moving bar.
For normal training, I have a squat rack with spotter arms attached. They are set just below the arched chest level so that they don't interfere with training, but I only need to flatten my arch to avoid getting my chest slammed. This is the safest way to bench.
I use a full grip for bench press, but I also have a somewhat narrower grip than those I've seen that use the false grip. However, I do use false grip on overhead work. It keeps the bar path over my shoulders where it is the strongest, and my wrists thank me for it.
I do recommend using wrist wraps if you use a false grip. I find it's more likely that the bar will roll toward the fingers than off the front of the palm of the hand. Wrist wraps provide additional stability so you can at least offload the bar safely and readjust.