I've done some deep dives with high level players on grips and what makes each one work and one thing many had was maximum set points or tight spots in the wrist for stability...which fingers you primarily grip with and which part of the wrist you lock or at least add some stability to will influence where your thumb points. As someone said above, starting with the idea of thumb down and working around that may not be right for you as thumb position is a result of how you get down over the shot and anything you do to set your grip in your preshot routine.
A little on the tight spots if u care to jump into some minutia:
1 - the most common grip thought was to let the hand be loose and hang naturally as it cradles the cue. For the vast majority of ppl, the thumb will hang str8 down with an empty hand. However, once the cue is in hand, if the guiding thought is to leave the fingers where they are to cradle the cue, the thumb rests against the cue and comes off pointing towards the body slightly.
2 - Pronators/cockers. Those who have a rotation in forearm causing pronation (palm facing back) have a str8 down thumb and some tension (or lets call it extra stability through the front side (thumb side) of the wrist. Another common way players add stability through the front of the wirst is to cock the wrist. The slight cocking of the wrist is probably the most common stabilizer I came across. Actually most said they have no tension and it just hangs but when pressed for where the wrist feels stable they point out the anatomical snuffbox utilized in cocking the wrist. These guys can be front fingers focused or back fingers focused and the main way you can tell them apart from the pronators is that with pronators the back fingers come away from the cue and play a smaller role in the stroke while with the cockers, all the fingers stay more in line with the cue allowing for more play from the last 3 fingers.
3 - Suppinators/Flexors. These guys are more rare but in good company with guys that have a slight internal rotation. Strickland, Reyes, SVB, and just about every single side arm and chicken wing player (good ones exist!) play this type of grip....The more face-on the setup rather than sideways, the more likely a player is to use this type of grip (again, HOW YOU GET DOWN ON THE SHOT sets all this thumb pointing up and probably why most responses in this thread include "i never thought about the thumb at all"). The portion of the wrist that adds stability for these players is either the back pinky side (esp for players that like to feel the cue in their last 3 fingers), or in extreme sidearm/chickenwing cases the flexion of the wrist is (palm towards forearm) is maxed out for consitency and stability while still alowing for a lot of back and forth writst action on plane.
4 - Extenders. Related to #1, when a person with the loose hanging hand that has thumb pointing down decides to anchor around the thumb and get the fingers out of the way rather than keep the fingers where they are and let the thumb rest inwards, one common way to accomodate this is to have a bit of overextension in the writst (what most ppl will see as flexion on the outside of the wrist resulting more in palm down than palm back). Players that play with a firmer grip or middle 2-finger grip will generally prefer this type of setup.
Like someone else said, a good few chapters can be written on this topic and still some iterations will not get covered. Generally though, I agree with the thought that grip results from your preshot routine, how you get down on the ball, the angle of your stance relative to shot line, and any sort of guiding grip thoughts you might have like pointing thumb down, pointing first knuckles down, second knuckles down, lock out wrist forwards/backwards, either side, etc. The important thing is, that whatever you do, keep doing just that and you will find consistency.