One thing that I always teach my students is that you never leave an axe on or in your axe block.
An axe can easily be knocked out and fall. A potential source of injury and a damaged axe. The axe belongs on the floor under the block or in its mask or holder, or may be on a large surface.
Have a look at these photos and you will see that bits of wood have stuck to the axe. If there is any moisture in the wood this can start rusting as well. These bits of wood are really stuck and do take effort to remove. The other problem with this, is that the could stop the edge biting into the wood. The skipping axe is another potential injury, very small, but lets keep the odds in our favour.
You will see that the axe in the above picture has its whole edge in the wood. I have been told by many different people about injuries caused by the tip only being in the block. The hand or a digit can get caught between the block and the inclined axe edge. Go on set your axe in a block and see what happens if you reach, for say, a knife on the block, not looking properly. The digit will get trapped and badly cut. Really not nice. Now who would set an axe in a tree trunk at 6 foot above ground? You know, to keep it safe. Do you want this falling on your head or shoulder? Again I heard of someone doing this and then stringing up a hammock on the same branch, caught his hand between axe edge and tree.
Personally I prefer cross grain blocks rather than end grain block. The axe does not get stuck in a cross grain block. More importantly it is harder to chop your axe into, so you are not able to store your axe this way.