It's evident that you're saying this as a non-European, as there's no "European healthcare".
Many (most?) European countries have private healthcare systems. Switzerland has it and offers some of the best healthcare in Europe and in the world. Similar systems work great in many other European countries as well. The problems with American healthcare are not because it's market-based, it's because how that market is managed.
Some other countries have public universal healthcare. It can work well, but it requires a high-income country with both wealth in abundance and significant government efficiency. It only truly works well in Scandinavia so far. This is not "socialist healthcare" as some will dubiously claim, it's sort of the opposite, which is why it works.
Many (most?) European countries have private healthcare systems. Switzerland has it and offers some of the best healthcare in Europe and in the world. Similar systems work great in many other European countries as well. The problems with American healthcare are not because it's market-based, it's because how that market is managed.
Some other countries have public universal healthcare. It can work well, but it requires a high-income country with both wealth in abundance and significant government efficiency. It only truly works well in Scandinavia so far. This is not "socialist healthcare" as some will dubiously claim, it's sort of the opposite, which is why it works.