But there is an aspect you are missing here.
Skills are yes/no. Everyone can do them. My barbarian can use persuasion, my cleric can steal with sleight of hand, my wizard can roll athletics. The number of proficiencies just tells me who is more likely to have a higher mod.
On the other hand, there are other balancing factors for spells, like the number of spells per day.
Every single first level spell caster (except warlock) gets two fist level spell slots. In fact, if you examine the chart for Clerics, Druids, Bards, Wizards and Sorcerers you will find that their spell progression and the number of spell slots they get is identical across all the classes.
All five classes get 3rd level spells at 5th level, and they get two 3rd level spell slots.
That is the balance point. Wizards have 397,106,410,874,542,000,000,000,000,000,000,000,000,000,000 possible spell combinations (ignoring cantrips and only counting the PHB), compared to the Bard only having 3,595,067,609,875,170,000,000. But both of them have an identical number of spell slots to utilize.
The designers didn't test every combination. What they did was decide that 3rd level spells should have X impact on the situation, then tried to balance it so all 3rd level spells were about equal, then limited the number of 3rd level spells that could be cast per day.
Yes, wizards have more options as to what that 3rd level slot might be, but the major balancing point is that they can only have so many of those spells, not how many options they have to place in those slots.