There are many different types of plastics. Some end up in nature as tiny pieces like you mention and are indeed very bad for the ecosystem. But it's also possible to set up a proper recycling & valorization system. Northern Europe already does it: over 98% of consumer plastics are either recycled or valorized through heat (producing power or city heating).

Despite that, there's an effort to address the low-hanging fruit of plastics that end up in the oceans and waterways, specifically single-use plastics: http://ec.europa.eu/environment/waste/plastic_waste.htm