if everybody votes, the government represent the interests of the whole population

This is simply false, representatives in the majority of neoliberal 'democracies' are not held accountable to the wishes of the people they are representing, and cannot be removed from their position with a simple majority from those who elected them, so then these people look towards those with influence (corporations, rich capitalists, etc) and then do things to please those groups in order to gain favor with them, like campaign donations, lavish luxurious trips and vacations, positive coverage in capitalist owned media, etc

(still disregarding lobbying)

Lobbying is not the only lever of power the capitalist class uses, the private ownership of mainstream media by capitalists means that all of their coverage would push capitalist interests, campaign 'donations' and funding is also used for control, to choose the candidates who represent your interest as a capitalist the best to win, and the candidates themselves are more likely to win if they come from a rich well connected upperclass background (meaning they are most likely capitalists themselves)

Regulatory capture is also a thing

There's also the fact that capitalists also fund think tanks to publish studies that support their interests (no matter how far from the truth they have to stray) and are then used to support legislation that is in their favor (see global fossil capital and climate change), there's also lots of astroturfing that goes on

And if lobbying were the issue, we could just ban it...

Even if you outlaw lobbying capitalists will still control the government in a myriad of other ways, capital flight being an example I didn't mention in this reply yet,but this one is very strong and the US/WTO/IMF enforce it on as many countries as they can, the only way to have actual democracy is through forceful suppression of the capitalist class, only then you could imagine having a government actually controlled by the people while still having a capitalist market and a capitalist class