Even if you somehow took care of the safety issue that others have mentioned, for example by staying with it the entire time making sure there's always enough water in it, there's a practical issue that stems from this point (taken from Pieter's answer):
Waste of energy, a water boiler is on or off, it will expend full energy keeping the water boiling.
This is an important issue that's gotten overshadowed by the safety issue. While the energy waste is one thing, it's not just keeping the water boiling (like you would when boiling water on a stove) but it's on full throttle all the time meaning it will produce a lot of steam.
Let's say you start cooking your pasta when the water is already at boiling temperature and it needs to be going 10 more minutes. Assuming a water cooker with a power rating of 2000 watt (which is common in the EU) that means you're adding 2000*10*60=1,200,000 Joules to the boiling water. Taking into account the heat of vaporisation for water that means you're putting in enough energy to turn 1,200,000 /2257=532 grams of water into steam (assuming all the energy goes into heating the boiling water and no other heat losses).
When starting on this answer I'd expected it to be a bit more, but consider that half a litre is still significant if it coats stuff in your kitchen.
In the US this is probably less of a problem as the average water cooker there runs at 1500 watt or so.