Apologies but you are mistaken. Cantrips are not based on a specific ability score by themselves. Cantrips are spells and in each classes spellcasting section it specifies what ability score is used to cast spells from that class. Example, firebolt can be learned by sorcerer (cha) and wizard (int) and they both use their respective ability scores to calculate the spell attack modifier for firebolt.

As far as what you are saying with eldritch blast, you are probably forgetting that eldritch blast is powerful for the warlock because of agonizing blast. Furthermore, the new version of the spellslinger uses intelligence instead of wisdom and has a much reduced spell list.

Indeed at 1st level, 5th, 11th, and 20th, you should find that the spellslinger does have an ability to increase the damage of a cantrip. So their bonus damage will look like this (spell mod * x) + (2 * x) at level 1 x = 1 and x increases by 1 at levels; 5, 11, 20. At level 20 their spell mod should probably be +5 so the bonus damage would equal 28.

The reduction of crowd control options is not a concern, if you look at this caster in the manner you would a martial. Indeed that is what I intended for this class that it plays like a martial character and what crowd control options does a rogue have? Or a barbarian?

It is not just spell slots that I avoided in this class it is also spell levels. That is the intention.