Li Shenron
Legend
Why doesn't the Wizard get proficiency in Arcana for free?
Why doesn't the Druid or Ranger get Nature or Survival?
Why doesn't the Beast Master doesn't get Animal Handling?
Because they are not needed. You can do the same things without the skill proficiency, you just don't get the bonus.
If you also want the bonus, use up one of your skill proficiencies. But if you don't care for the bonus, maybe because you already have a high ability score, at least you can choose.
Most players will choose that iconic skill proficiency anyway, that's true. That means that maybe the PHB should really grant all wizards fixed Arcana proficiency + one skill of choice. Just like it could have been better, it could also have been worse. So maybe the current rule ain't that bad.
And by the way, I have played both wizards without Arcana and clerics without Religion skill proficiencies and they were fine.