Hard Mode Primals of the 'original' three Primals are actually a side storyline (part of a post main scenario storyline listed in the Journal as 'Chronicles of a New Era' which also includes the quest line for the Binding Coil of Bahamut and the Crystal Tower), so they're actually optional. However, they are mandatory if you wish to gain your relic weapon, as the first three HM Primals (Ifrit, Garuda and Titan) must be defeated to complete your relic quest).

Having said that though, the 'new' Primals added in the 2.1 and 2.2 patch storylines (Good King Moggle Mog the XII and Leviathan), don't have a 'SM' form - their 'Story Mode' form is 'Hard Mode', but it's somewhat of a misnomer as they're still reasonably easy to deal with. I haven't unlocked the EX Mode Primals though so I have no idea exactly how difficult those are from first hand experience, but I've heard the horror stories.