Not to put too fine of a point in it but you're wrong because your understanding of frame generation and displays is slightly flawed.

Firstly most people's displays, whether it be a TV or a monitor, are at least minimally capable of 60hz which it seems you correctly assumed. With that said most TVs and monitors aren't capable of what's called variable refresh rate. VRR allows the display to match however many frames your graphics card is able to put out instead of the graphics card having to match your display's refresh rate. This eliminates screen tearing and allows you to get the best frame times at your disposal as the frame is generally created and then immediately displayed.

The part you might be mistaken about from my understanding is the frame time lag. Frame time is an inverse of FPS. The more frames generated per second the less time in between the frames. Now under circumstances where there is no VRR and the frame rate does not align with a displays native rate there can be frame misalignment. This occurs when the monitor is expecting a frame that is not yet ready. It'll use the previous frame or part of it until a new frame becomes available to be displayed. This can result in screen tearing or stuttering and yes in some cases this can add additional delay in between frames. In general though a >30 FPS framerate will feel smoother on a 60hz display than a locked 30 FPS because you're guaranteed to have every frame displayed twice.