They were just containers so the width of the opening is irrelevant.
It was a thing to be broken when thrown - why bother finishing off and polishing the rim?
That is just a lot of extra work and expense. I have seen Ysart ones - which are really quite crude and it's only because of seeing them that I recognise what yours is.
We might have images of one somewhere here - I'll have a dig.
Your Dad knew what he was talking about.

eta.
I've found a thread on these, but sadly the reference link to a catalogue has vanished. You might be interested in the chat which describes uses and folks' memories of them.
http://www.glassmessages.com/index.php?topic=17487.10HOWEVER - I may have spoken too soon!

That link got me to the site Scotland's Glass, and I had a dig around there. I may have found your wee bottle - and according to this, it IS a target thingy - to be filled with feathers and shot at. So they still would not have to be finished off nicely and a wider neck would be easier to stuff feathers into - see the photographs here.
https://ysartglass.com/Moncrieff/MoncrieffProduct.htm