Destroying agencies that give research grants will do nothing to address the systemic problems academia has with the publish-or-perish model, or the exploitation of graduate students, or anything else.

It will result in people losing not only the valuable career opportunities presented by government-funded fellowships, but also their jobs. Younger faculty members without the protection of tenure suffer when budget cuts come around, and in a dire enough situation might face termination. Without the relief from teaching duties provided by fellowships, graduate students have to work that much harder, and without the opportunity for travel that reasonably small grants can provide (we're talking money on the order of 10000 USD or less, often) dissertation research that isn't entirely local is untenable for all but the independently wealthy. Adjunct faculty and lecturers, whose positions are always tenuous, will lead even more uncertain lives, should these agencies and their programs be eliminated. So will the staff who support academic departments, who do valuable and necessary work that is often taken for granted.

You're right that academia faces systemic problems. Breaking things isn't the answer.