Besides externalized costs, which is gigantic issue that is not easy to solve. These problems are also clear market failures:
Large scale goals with large public benefits but which come at high costs will not be achieved without high level cooperation. For every individual market participant, the public education system, the public highway system, the public energy system, etc. have costs far exceeding their means. Yet every market participant benefits enough that they are happy they exist. The level of cooperation needed requires organization at the scale of at least local government.
Dealing with external factors, such as other nations -especially if they're hostile- or natural threats. Individual market participants can not muster armies (unless they are at the scale of governments), cant bargain with foreign governments on equal terms and will not provide (preventive) care for disasters/diseasese/etc. Would microsoft or walmart vaccinate everyone?