Do people *need* lessons in Art, History ect anyway? The elite would still make sure their children got those lessons and it would prevent the clever members of the working class from competing with the rich.
It's not as if history or art was banned-people who wanted to could still study/do it as a hobby.
Don't be so quick to dismiss the more... Well artistic aspects of education. Again, diversity of education produces diversity in thought. Education isn't only about teaching facts, it's ideally about teaching a way to critically assess the world around you.
Studying history may teach you the date of the American Revolution, but it can also teach you important critical assessment skills such as judging source bias, an incredibly useful skill in a media saturated world.
In the same vein, studying English can tell you the story of Romeo and Juliet, but it can also teach you the ability to critically assess literature which can translate into critical thinking in other aspects of you life.
Schools should also be a place where individuals learn their own strengths and areas of interest. Personally arts, classics and history were infinitely more beneficial for furthering my own growth than science, maths or IT, and for other I imagine the opposite is true. Variety gives opportunity.
In this proposed scenario, having less options available is probably going to encourage more drop outs as there are even less areas that a prospecting student can try and find an interest in. Assuming this is a still a democratic, Western nation as per the OP, I cant imagine the government that puts this into play is going to last long. The social impact alone is going to cause headaches.