Why do most restriction enzyme cuts at palindromic sequence?
Because it is more efficient.
Enzymes such as restriction enzymes have to recognize a very specific sequence in order to carry out its task. It binds to the DNA only in one specific configuration. Luckily! because you don't want a 'pacman' that cuts DNA at random places.
DNA is double stranded, so it has 'two sides' to which the enzyme can bind. A palindromic sequence is the same backwards and forwards on both sides (see image below). This means that the enzyme recognizes the sequence no matter from which side the enzyme approaches the DNA.
A palindromic sequence also increases the chance that both strands of DNA are cut. It is even possible that two enzymes work as a dimer to cut the palindromic sequence, further increasing efficiency.
The last reason has been important in the struggle between viruses and bacteria. Bacteria have evolved to 'disable' bacteria-targeting viruses (bacteriophages) using restriction enzymes that bind to these palindromic sequences. Cutting both strands of DNA harms the virus more than cutting one strand.