@BananowyJE
That would not make sense. It has already been explained that at a certain age, people are granted a class. This grants them mastery over certain passive abilities and techniques. He was never granted any mastery of any technique. This was shown when he started learning swordsmanship and even explained further by his father when he explained how skills are performed: they're done automatically. However, in this world, everyone can still study, train to learn new techniques and evolve their classes, though most appear to have poor understanding of this and instead of gaining a deeper understanding tend to limit themselves to what they were granted.
He's simply learning all the techniques from the very bottom as someone who was not granted any particular talent in the form of a class. In the last chapter, he even made a note that after 6 months of training his mana, he was finally at the same amount as someone of the sorcerer class which is the starting line, except that he still had no magic skills to use that mana so he still needed to learn that. And then it skipped over to him using all types of magic at intermediate level.
All in all, it simply doesn't make any sense for him to have all the classes. That said, having no class does not make him untalented and he is clearly a genius. It may also be that being classless actually grants him a boost in learning speed. He also doesn't appear to have any restriction as to what he can learn.