I guess it depends on the company culture a bit (do people under you have equity?), and it seems like you want equity as opposed to choosing a higher salary with no skin in the game, so that helps.

But if I found out and I was working for you, I might question how much you care about making the company successful. You've already said the salary is not competitive, so without equity; you can easily pick up and leave as soon as you find a better role. Maybe reading the comments in this thread will even make you realize this; you could be at a new job in less than a month.

I think I can say this isn't just "your" problem - you've stated the situation is demotivating and you are not giving it all as CTO; passing over "great ideas". Being unmotivated at work is a personal problem if it bothers you. Passing over great ideas or changing jobs is a shareholder problem, but that doesn't include you. It would potentially be something to bring up to shareholders especially if you are prepared to leave over it.