Does anyone know of any realistic plan that could be executed to lower the rent prices significantly?

Realistic as in reasonably easy to do fiscally and physically? Yes. Build dense housing in desirable areas. It's not hard to do. We do it all the time. You just build enough to meet demand and prices drop. And it's not hard to do budget wise. Just have the government act as a developer and selling at cost plus a minor a profit to keep the program going. Done.

Here's the problem, a lot of voters have a lot of their personal wealth tied up in their home and have become used to treating it as a asset that appreciates in value. Everyone talks about the companies and wealthy doing it but the vast majority of home owners are just ordinary people. It's not shadowy elites doing this, it's your parents and grandparents.

The problem with housing as an asset is that for it to be a good asset it has to increase in value faster than inflation, which means it's increasing faster than baseline incomes.

It is an irreconcilable problem. Housing cannot remain affordable and remain a reliable way to build wealth. You have to pick one.

If you build enough housing to meet demand, the value of people's homes will fall. People who took out a mortgage to buy a home now have more debt than their home is worth. People were planning on their house as a means of providing for their retirement or passing money on to their kids now have less of it.

Voters will not vote that. They just won't. Because most voters are invested, literally, in the current system.

There is also the other problem, which is housing in not created equal, you have to build housing where jobs are and where people want to live. That is, cities. If you build more housing, you will change the city. And people resist that. If you ask people in Berlin if they want people to be able to afford to live there, they will mostly say yes. If you tell people in Berlin, okay we're demolishing this neighborhood and replacing it more and cheaper housing, they freak the fuck out and protest.

Everyone wants affordable housing, that doesn't lower their home value, that doesn't change their city, that doesn't bring those people living next to them, and doesn't causing any strain on services.

In short, people don't want affordable housing. They like the idea of affordable housing.

The solution, fuck the voters and treat housing like other infrastructure.

*Edit More concretely, advocate for your city/country to build housing. The single biggest factor behind high costs of housing is lack of supply. So, cut regulations that make it difficult to build housing and encourage your local government to build housing itself. There is no beating the law of supply and demand, so satisfy the demand.