That's different from how menu icons apart have been used clasically. In e.g. Microsoft Office the save icon was present in the File menu along the text, and also the toolbar, stand-alone.
And it was clear enough that you would trust the stand-alone save icon to perform the action you expected. Icons were also selectively chosen for common actions.
If icons are considered non-deterministic and non-canonical, then they can't [confidently] be used stand-alone.
Also, I'll meet your data point of 1 with mine. I have an iPhone and find it far easier to pick an app from the list of names than pick an icon. I frequently mix them up (and I only use a dozen routinely)
And it was clear enough that you would trust the stand-alone save icon to perform the action you expected. Icons were also selectively chosen for common actions.
If icons are considered non-deterministic and non-canonical, then they can't [confidently] be used stand-alone.
Also, I'll meet your data point of 1 with mine. I have an iPhone and find it far easier to pick an app from the list of names than pick an icon. I frequently mix them up (and I only use a dozen routinely)