I feel for the compact camera manufacturers. Smartphones killed the 2/3" sensor market. Now they've killed the 1" sensor market too. Micro 4/3 is stale with no major sensor advancements for years now. What's left, APS-C and up?
If you compare like to like, same sensor tech, same quality glass .. there is absolutely no way a tiny sensor can out-resolve or out-perform a larger sensor when it comes to image quality. There are other metrics where it can - for e.g. power consumption/heat output, ability to stabilize the sensor (smaller = easier), faster readout (generally easier on smaller sensors), etc.