Can't Place Tone Curve Markers In Lightroom Classic v 7.3.1

If you have a version that supports this, there is a small square button at lower right of the Tone Curve panel which switches it between slider mode (pre-defined, named tonal zones), and the free points mode you are looking for. Each mode has its own, quite separate parametric settings that recall when you switch.

In slider mode, interacting with the curve is the same as dragging, or typing a different value for, one of the sliders below and that is all you can do. Points mode has no such predefined sliders to limit it.

Later versions offer a slightly different interface with buttons above, adding a more direct way to access R G and B.

FYI Tone Curve is applied cumulatively onto a 'flat' result of the Basic panel tonal settings as they currently stand, therefore cannot itself e.g. retrieve lost highlights. For the same reason, Tone Curve can show a coarser result especially with fine tonal gradations, compared with achieving the same tonal manipulation in Basic.

That said, if being applied for a specific consistent "look" across many images then Tone Curve's independence from their necessarily very individualised Basic panel settings, can work to its advantage. As, when (say) a 'cross processing' look is applied, we are expecting this to in some sense deliberately 'degrade' these images from how they may be each technically, if perhaps boringly, optimised 😄 .