Because then the money just moves to whoever does have influence on how the republic is actually being run. Or, worse yet, the money just buys the power it was

Because then the money just moves to whoever does have influence on how the republic is actually being run. Or, worse yet, the money just buys the power it was previously trying to influence and simply wields it directly. Weakening the formal power of government officials doesn't make that power dissolve, it just displaces it to somewhere even less visible and answerable to the public.