Disadvantages

Here's some of the disadvantages of splay trees.

A big one is that there is a possiblity of a tree having linear
height, which is something that other trees always
prevent. Another disadvantage is that the we normally think of a
search operation as nondestructive, that is, it doesn’t modify
the tree, but in the case of splay trees, it does. The most
obvious situation where this can become an issue is in a
multithreading environment. Finally, splay trees have the
disadvantage that individual operations can be expensive.  For
example, it is possible for a search to take time O(n) the
first time it runs, then O(1) the next time.