Would A Track Shuffle App Be Useful?

The icon shows the icon of the linked default application, the one that is opened if you select "play".
It does not reflect the filetype as such. And as it is related to "playing" I do not find it too far fetched to lead to a random playing order.
If the default application is also default for other filetypes, then the same icon would appear although it is a different type of file. AFAIK this icon is taken from the OS:
Please note also that the randomizing function was attached to that column header long before it was finally added to the column menu:
[2020-10-20] NEW: added option to randomize sorting via menu "View > Sort by". (#11763, #50519)
and for backwards compatibility reasons that special column header still behaves in the old way.

To sort accurately by the filetype, you would still need a dedicated column.