I think it would take tremendous political capital to do this. Every favored tax treatment would be a hill to die on and there's a risk that the opposition woukd win on a platform of adding some back in, destroying precedent against changes immediately.
So you'd not only have to win the battles, you'd need enough manpower to occupy the territory once the dust cleared. That occupation will last for a couple election cycles at least; in the US it would be best done by an incoming president popular enough to have a good shot at re-election after.
I suspect it will take an extended time of economic malaise to kill the 'trickle-down' mindset. After all, this mindset took root in the western hemisphere during the time of Reagan and Thatcher (read, 80's) and the Horatio Alger myth remains extremely attractive to the temporarily embarrassed millionaires which keep cutting themselves by voting the right - at least the non-progressive part (is there such a thing as a progressive right?) - into power.
[As an Asian, this myth is actually far stronger in this emerging, newly industrializing region. But there is a potential for people to quickly lose faith in it.]
Yes, the best solutions are to eliminate the Mortgage Interest Deduction (which definitely won't decimate the already critically wounded housing industry) and Employer-Provided Health Insurance Deduction (which definitely won't push millions more people out of health insurance, "forcing" insurance companies to increase their rates to maintain their margins and inefficiencies).
So you'd not only have to win the battles, you'd need enough manpower to occupy the territory once the dust cleared. That occupation will last for a couple election cycles at least; in the US it would be best done by an incoming president popular enough to have a good shot at re-election after.