Just one more post before I take my summer break...
Trying to tuck your thumb under other fingers when playing piano does not seem right to me.
*In the first place, it cramps the hand.
*Secondly, it makes the elbow flay out.
*Thirdly, you've tucked the thumb under the third finger. What is the next finger you have to use? That's right, it is the second finger. Where is that finger? It's way to the right (on the right hand) and above the thumb, so you must bring your elbow back in and swing that finger over the thumb so it is in position to play the next note.
Instead, what I do is to simply move my whole hand over in one continuous motion. Then then the thumb and all the other fingers are perfectly positioned to play the next notes. I learned this from a you tube video. I just read that Charles Rosen did that too, and could play that way legato. If it makes sense for you to tuck the thumb, don't let me stop you. For me it is a disaster and makes me think of my childhood of keyboard awkwardness.