In reply to simondgee: Interesting question.
In terms of teaching belaying, I witness no end of novices making a hash of it and regularly twisting, inverting and otherwise cross-loading their belay krabs.
How quickly novices master basic belaying varies massively. With some appropriate instruction, the majority quickly get to the stage where they can generally maintain the belay krab in the correct orientation and position without excessive movement but a small minority do struggle and have issues that persist well past the first few times they belay.
I wouldn't say there is a big safety issue as regards belaying but using a Belaymaster etc. will make things easier for those novices who both take a lot longer to get to the conscious competence stage of belaying and who then struggle to get to the stage of unconscious competence. Equally it may also make it a bit easier for instructors who are supervising such belayers.
However, I don't think it would appreciably improve the safety of experienced belayers though. There is a potential argument they can improve a belayers' situational awareness as they can spend more time looking at the leader and less checking their belay krab but I am not wholely convinced by this.
But where there is a massive safety issue is in the use of karabiners to connect the rope to climbers rather than tying in. There have been numerous recorded injuries across Europe resulting from standard screwgate being used in this manner and then subsequently becoming detached. There is long standing UIAA guidance note about the risks of this.
As mentioned in the article and my previous post, using a DMM Belaymaster greatly increases the security of this method of attachment. For example, I routinely use a Belaymaster for connecting the safety rope when I need to safeguard an abseiler.