That hole in the bottom of the cleat is NOT for passing the eye through. It's purpose is to reduce the amount of metal used in the cleat and therefore reduce the price. Also a line correctly sized to the cleat won't fit through there on many cleats. Years ago my father did about the same thing to one of his fingers, didn't cut anything off but did sever tendons, nerves, etc. Basically lost the use of the digit, it just flopped around. He'd have been better off of had just been cut off.
It's not just a personal safety problem, with the eye passed through the cleat there's pretty much no way you can release the line with a big load on it. You'd have to cut it loose in an emergency.
Instead of looping them through like that, I splice my eyes so that they barely fit over the cleat. You can usually pull in enough slack to lift the eye over one horn and release, and they don't come off by themselves. If you have premade eyes that are too big, you can add a whipping to reduce thier diameter. Of course a line made up with a cleat hitch, no eye at all, can be untied no matter how much strain is on it.
I've seen the eye-through-the-hole thing recommended in boating text books, I pretty much stop reading at that point as the author just proved he doesn't know what he's talking about and I can't rely on anything else he writes.