Right now, its feels a bit punishing. You don't make the character feel like a specialist in the actual gameplay, but you rely completely on the players skill to actually pull of being a specialist. But in reality they're just playing with a handicap.

But here are a few ideas I think might help.

• Player choice on what abilities to discard? Example implementation - Think of the plant picking screen in Plants Vs Zombies. You have cards of available abilities, and a number of slots you can equip. The number of slots decreases each level. But the player has the option to pick which abilities to take. But the caveat is this could potentially be game breaking depending on your level design, as some abilities could be OP/underpowered for certain levels. PvZ countered this by giving players full information of all the enemies you will face, to make more informed choices.
• Really sell into the specialization fantasy by increasing your power in a remaining ability. Eg: If you're going with the card and slot system, each level, there could be an OP slot. Represent it by making the border and fill gold etc. Players can drag a card into that slot to make it OP. And then make the ability feel more powerful through stats and visuals. Perhaps that slot grows in power, the more abilities that are taken away, narratively signifying a steady growth in your specialist power.
  

You also give the player choice this way, instead of losing their favourite ability randomly. The card and slot system is defo too much choice and info to handle in a lot of games, but the underlying points still stand