What is disadvantage of using CART in regression problems?
Regression and classification trees are nearly identical in how they function. I'm not aware of any specific downside to regression trees specifically. However, trees in general do have the downside of being susceptible to overfitting:


  The main downside of decision trees is that even with the use of pre-pruning, they
  tend to overfit and provide poor generalization performance. Therefore, in most
  applications,...ensemble methods...are usually used in place of a single decision tree.


Muller &amp; Guido, Introduction to Machine Learning with Python, 2017.