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They're bad because they can split at any time. They're called widowmakers because they have the potential of exploding when the tires are mounted and filled with air, thus killing the technician working on them. Yes, you should replace them as soon as you can.
Our resident wheel expert, Stu, will likely be along shortly to explain more in detail.
More to your present situation, if the tires get low on air, there is a certain amount of risk when adding air to them. If they get low enough that the pressure doesn't hold the two halves together tightly, let all the air out and take the wheel off and to a shop where it can be inspected and worked on in a cage. For instance, tire goes completely flat with the truck's weight on it -- I would not inflate it!!
The 17" wheels used on the F-3s and F-250s are called "widow makers" (WM) because of the way the wheel halves assemble. While many multi-part wheels have an outer ring on the face of the wheel that holds the assembly together, these 17s have their connection point along the midline of the rim. This makes it hard for the technician to see whether the halves are fully connected, which creates great risk of injury to the tech while airing the tire. They also can flex at the joint while in service which can lead to violent separations. Then you compound that with rust and 60 years of abuse/use and you have a wheel that very few reputable shops will touch anymore. I'll post pics below of the assembly so you can see what it's about.
Since you have a '53 F-250 you have it easier than many members who are looking for replacement wheels. Any 16" F-250 wheels having the 8 lug x 6.5" pattern, up to the 1997 heavy duty model, will fit your truck. If you want to use the factory hub caps, you'll want to look for the F-2/F-250 wheels that were used from 1948 into the 1960s. These, and many others, are one piece designs. Below are pics of the WM. Stu