Why not have Pitot Heat always on?
I can generally only speak for commercial aviation. The reasoning is probably the same or similar for General Aviation, but seeing as that is such a wide and varied field, with a tremendous number of different aircraft, probe types, etc., someone somewhere could probably find some niche corner-case to dispute the reasoning. My guess would be that, generally speaking, in General Aviation, certain probes are most likely only meant to run for a certain period of time. After all, it's not like a Piper Cub is going on an 18-hour non-stop flight to China like a Boeing 777 might. I'm not saying that a probe will fail after 18 hours of being on, just that repetitive use in that way might necessitate a different type of probe with a more robust design.

In commercial aviation, many modern airliners use certain logic to turn pitot heat on or off. With the exception of a manual override switch equipped on some aircraft, to force it off, the pitot heat is generally on during most flight phases and works as such: 

On the ground, with engines off, the pitot heat is turned off. On the ground, with engines running, pitot heat is on low. Finally, once the plane takes off, the pitot probes are put into a "high heat" condition and remain that way for the remainder of the flight (unless manually turned off). 

The pitot heat is generally monitored with current sensing relays such that if the pitot heat draws excessive current or not enough current, the crew will be alerted to a pitot heat failure. 

Why not keep them full hot all the time? For one, that would most likely cause premature failure of the heating element. Another reason is that, on the ground, pitot covers are normally applied to prevent bugs from building homes inside the tubes as well as preventing other debris from entering. The pitot covers will melt and destroy the pitot probes if the covers are left on while heat is applied. This can also be problematic and dangerous if the pitot cover partially melted, wasn't noticed by ground crews, and the drain holes or entry holes were blocked by the melted cover. Finally, and probably most importantly, the pitot probes get extraordinarily hot. Speaking from experience, and from having touched one that had failed in the "full hot" phase, it takes only a brief second to receive excessive burns on one's hand. Most of us that have been around them in our lifetimes have been burned by them, and a savvy mechanic will always approach them with caution!

So, it makes sense to have the probes off, on the ground, with engines not running. Otherwise, commercial aviation has more or less decided that "full hot" in the air, and low heat on the ground with engines running is a design characteristic.