The triangle of thumb, 1st finger and 4th finger on the bow is important for many bowstrokes, especially those that involve lifting the bow into the air, such as down-bow retakes and spiccato.
The 4th finger needs to be able to help support the weight of the bow in the air.
Tapping fingers will help you improve your bowhold. In the lower half of the bow, the 1st finger generally should not apply pressure - you can check if the 1st finger is pressing by lifting and tapping.
A flexible thumb is vital for all bowstrokes. If the thumb is bent inwards it cannot move; however a thumb that is extremely curved may also lack flexibility.
Just as suspension in a car ensures a smooth ride, so flexibility in your bowhold helps produce an even sound. You don't jump on a trampoline without bending at the knees!...