Not everywhere. Most of the industrialised world does not build new combined sewers. So if you live in a city that didn't exist say, fifty years ago, the storm water sewers and foul water sewers have always been separate, and as a result there's no Combined Sewer Overflow.

Some US cities in the middle are like this, nobody (to a first approximation) lived there in 1901, and today there may be a small city with an airport and a decent night life. But in Europe, and on the US coasts, the cities are older.

In theory, you can separate existing combined sewers. For a town you could maybe attempt this as a large local infrastructure project over the course of a year or two, in a small city this is a large and expensive project that could take decades to complete. For somewhere like London or San Francisco it's unthinkably costly and won't be attempted in the foreseeable future.

A small sign of willingness to attempt this, combined with the difficult reality of such work goes like this, I live in Southampton, an important port city on England's south coast:

1. Legally, if you fit a new grey water waste (e.g. from a shower, or a washing machine), it should flow into the sanitary sewer, which your home is plumbed into usually via large black pipes that run mostly vertically up the side of the building. It must not flow into the storm water sewer, which is often smaller rectangular pipes connecting to the gutter where they collect roof water.

2. But, there's probably a gutter pipe right near where your waste is, while the sanitary sewer could be on the far side of the property. So, does the plumber do the extra work, and charge you for it? Or do they just cut into the storm water sewer and save their time and your money?

3. Result: Now if you separate the storm water sewer, it has grey water waste flowing into it, and you're dumping that into the sea. Oops.