It's an interesting question. I'm not aware of any 'official' reason as to why the York town mark was so rarely used on smaller items, but I can think of at least a couple reasons why these pieces lack it. It was perhaps considered excessive for smaller items to be struck with six marks, it is to be remembered that with every striking of a mark, damage occurs to the item, which has to be corrected by the silversmith upon their return, the smaller the item, the more damage would have been done (there was much grumbling in the trade during the period of double duty marking) and more effort on the part of the silversmith to put things right. On small items the profit is perhaps minimal and time spent refinishing items resented.
The larger the punch, the more force required to make an impression. Although it does not show up well in these images, the cross is surrounded by a circular cartouche. It may well have difficult to make smaller town mark punches at this time, to get the detail of five lion passants into the punch must have challenging to the engraver. This punch may well have been the most costly to produce and consequently its use minimised to spare expense.
Just thoughts, and it would be good to hear the thoughts of others.