The problem with a sightseeing log style menu for minions and mounts is the fact that there are a number of minions and mounts that are now completely unattainable (and will never be made attainable again), like the Legacy Chocobo, 1.0 Gobbue, Wind-Up Dalamud, Wind-Up Bahamut etc, thus this would mean if you haven't got these minons and mounts it would leave 'gaps' in the listing that would always be there, taunting the player subconsciously and frustrating them to no end. As areas listed in the Sightseeing Log are always open and always attainable, thus it means it never has this problem. Thus I don't see SE adding this I'm afraid.

As Istaru mentioned, there are plenty of websites online that list all the available mounts and minions and how to get them if you've lost track of what you haven't found yet - I personally use Gamerscape's minion and mount pages myself.