[ST1100A]

The hole in the blade is too big for the blade spindle. The Hex on the spindle is for a washer that presses up against the blade, then there will be a cupped 'spring' washer that goes against that, then the bolt with lock washer.
Some spindles have a mount piece that has a larger 'boss' or raised ring area on them to hold the blade centered, so check to see if it has that, or it's worn off, or maybe it was lost, and a different piece was installed.
That raised area is not much, about half the thickness of the blade, and if the blade bolt ever comes lose, it could cause the blade to wobble, get out of center, and wear off the raised part that centers the blade, same with the 'hex' piece that is used for the hex washer. That is used to help grip and spin the blade, but lets it slip if it ever strikes something to help prevent damage to the spindle and other parts.
The spindle shaft could have been replaced with the wrong part in the past, and the blade was never mounted properly.
Simplicity did use many different spindle parts over the years. That's why you need the deck part number, or the package number as long as it was the original deck that came with the tractor, in order to get the correct replacement parts for it.
A lot of the parts will interchange somewhat but could cause a problem if all the related parts are not used with them if anything was ever changed from original.

 

[ST1100A]

The 'Shoulder' is worn off of the spindle right below the 'Hex'.
They do wear down, usually from a loose blade.
He will need to replace the blade spindle shaft. They are a common wear item, along with the spindle bearings.
They are not expensive for the parts to rebuild the spindle. Most times you can get the entire spindle assembly. They are a little bit more expensive, but then everything is new, shaft, bearings, housings.
They are the wrong blades on it now. The center hole is way to big. Simplicity uses a much smaller center hole on that model deck.
Usually you have to get the blades from a Simplicity dealer. Some decks use 2 different size blades on the same deck. Some decks use 'Low Lift' mulching blades, some use 'High Lift' bagging blades, some use General Purpose blades. They did make optional blades for most of their mower decks besides the standard blades.

 

[ST1100A]

your second photo shows a stepped washer, does that step fit inside the blade?

That is actually 2 washers together. The 'Hex' washer and the 'Spring' or 'Cupped' washer without the 'Cup' in it anymore.
The 'Hex' goes on the blade, then the 'Spring' or 'cupped' goes on next, then the bolt.
He should replace the 'Spring' washer because it is flattened out and won't lock the bolt anymore.
The 'Shoulder' on the spindle shaft is just a very little bit larger than the 'Hex' on the spindle shaft.