To Benny's point - "The best argument that I have heard for powering bilge pumps 24/7 is "If they can save the boat or not; what do I have to loose" and my answer is "the battery bank".
A complete discharge of a battery, once, does not destroy it. It's not good for it, but it does not destroy it. If you can charge it fully, run a good equalization step on it, it will still be in decent shape. Now, you don't want to keep repeating this or you will destroy that battery.
But from my perspective, I'd rather take the statistically small probability risk on a one-time dead battery due to a malfunction of the circuit and keep the security of the bilge pump turned on helping against water ingress that protects my boat, it's interior etc. I think the statistical probability of me forgetting to close a window, a seal getting something stuck in it allowing a leak, a through hull that's decided to start leaking, a hose connection that is starting to weep, etc. etc. is far greater than the bilge pump circuit going crazy and draining my battery.
The statistical probabilities surrounding the number of potential failure modes are far greater in the scenario of not having the bilge pump turned on than the essentially single failure mode of the bilge pump circuit failing, and discharging a battery....
Of course, neither of these fully protect you from some sort of catastrophic failure. However, keeping the bilge pump on does provide a greater level of security than keeping it off.
This logic says you would rather lose the boat than some consumable batteries??
A sticking float is pretty rare I would think.
I've found two main failure modes for pump float switches, they stop turning on, or ther float can get stuck on - meaning the float came up high enough due to water ingress, something made it stick in the up position and then you can run down your battery.
In the first case, since the boat is a dry boat, who cares? In the second case - well - you just found out your boat isn't as dry as it should be.
I can't see a solid logic to not keep your automatic bilge pump turned on, especially if you have one in place. If you don't have one, and you have to go through the expense of installing one, then I could see arguments supporting not do that as viable.
dj