The reason for the idea of leaving the boiler on all the time is to prevent corrosion within the boiler. When you leave the boiler off, it is not circulating the treated water that has the necessary chemicals to counter oxidation. Many boiler systems will either preheat the water or inject an oxygen scavenger to reduce the oxidation to the boiler metals in contact with the water. The reasoning behind leaving it on all the time in an idle or low fire state is to keep the water hot, which also reduces the oxygen in the water. While ON, it would also be circulating the needed chemicals to protect the boiler inside.
The truth is leaving your boiler ON all the time is expensive. Especially when you factor in the cost of rising gas cost. I don't know how many hours a day you are running your boiler, but they make low water content steam boilers that are able to go into standby, or be off from a gas/combustion perspective, but be ON connected to power and alive to the system saving gas. Depending on how long you leave your system OFF determines what kind of layup procedure you should take. The trick is to spend the money on the proper water treatment and chemicals because that will do the best to protect your investment. Then you can turn the boiler off when not needed to conserve fuel and runtime and the inside will be protected by the chemicals and deoxidizing procedure.