The government is tied to the mode of production, it isn't above it. When capital owners hold sway over how society functions, it isn't through bribes alone that this happens. Control of media, control of the state, administration, cultural hegemony, etc all influence it. As such, no direct democracy could really exist in capitalism.

Even an honest and well meaning politician will be blocked at every step. Like corporations and big businesses sabotaging key supply chains, media engaging in character assassination, and if all that fails then either a military coup or a literal assassination (like they did to Salvador Allende in Chile). Unless the politicians try to gain concessions from the ruling class in exchange for complacency, which means we still have our status quo.