If every problem is a nail, the only tool you need is a hammer.
The Cycle Stop Valve has saved a lot of pumps when the bladder tanks busted. In 1995 I let a salesman talk me into trying a new brand of pressure tank. This tank had a bag instead of a bladder. If it ain't broke don't fix it. I should have known better than to switch from a tank that had served me well for decades. Within a few months these bags in the tanks started busting. However, I had already installed 86 of them before I new there was a problem with the tank. Thank goodness I had also used a Cycle Stop Valve on all of these systems.
Yes, when the bladder or "bag" is busted, the pump will start as soon as you crack the faucet open, and shuts off as soon as you close the faucet. This is exactly the way most of the variable speed pumps operate, and no it is not a good thing. Without a Cycle Stop Valve, these pumps would have cycled on and off rapidly as long as a faucet was open. If you have ever watched a pump cycle with a waterlogged tank, you know that it could cycle every second or two as long as a faucet is open or the shower is running. This means the pump could cycle hundreds of time while you are taking a single shower. When the system has a Cycle Stop Valve, the pump will start as soon as you turn on the shower, and the pump will stay on as long as the shower is on. Turn off the shower, the pump immediately goes off but, it doesn't cycle WHILE the shower is on. This will help save your pump until you can get the tank fixed.
Since many of the 86 of these systems I installed also failed basically at the same time, I was unable to get to many of them for several days and even weeks for repair. It was a big job to warranty 86 systems at the same time that I was trying to do my regular (scheduled) jobs every day.
Many of these systems had run with the waterlogged tank for weeks or months before I was aware of the problem. Most customers did not even know there was a problem. As soon as I was aware of the problem, I called all 86 customers and ask them to run a 1 GPM hose in the flower bed or garden, until I could get there. Knowing what I know now about Cycle Stop Valves, I would no longer even worry about running the 1 GPM. After replacing all 86 of these bad tanks, I was amazed that not a single pump out of 86 systems had been destroyed. There was not even a single capacitor blown.
This proved two things to me. The first is that when using a Cycle Stop Valve, the size of the tank was not nearly as important. The second thing was that when using a Cycle Stop Valve, the systems were much safer for the pump even if the bladder tank is waterlogged.
Since that time I have learned that there are many other benefits for using a Cycle Stop Valve. Pumps, motors, bladder tanks, check valves, pressure switches, and everything else in a pump system last longer when using a Cycle Stop Valve. Using the Cycle Stop Valve saved me many, many thousands of dollars not having to replace all 86 of these pumps. When using a Cycle Stop Valve even starting capacitors do not blow, which is a first sign of rapid cycling, NOT A SHORT.
BTW, pump hanging by a thread tells me that you probably had galv pipe threaded into a brass check valve. If you simply rap this connection with electric tape, it will prevent the electrolysis that caused the pipe to be eaten off just above the brass check valve.