- ID3, CART, C4.5, and C5 are all conceptually equivalent "recursive partitioning" algorithms, and CART is sometimes used as a catch-all term instead of the phrase "recursive partitioning".
- MARS requires two passes over the data
- CART is "dumber" than CHAID, which could be seen as a benefit for "high-volume" ensembles like RFs and GBMs. One blogger writes that CHAID is a better explanatory/exploratory tool, while CART is a better prediction tool: http://www.bzst.com/2006/10/classification-trees-cart-vs-cha...
- ID3, CART, C4.5, and C5 are all conceptually equivalent "recursive partitioning" algorithms, and CART is sometimes used as a catch-all term instead of the phrase "recursive partitioning".
- MARS requires two passes over the data
- CART is "dumber" than CHAID, which could be seen as a benefit for "high-volume" ensembles like RFs and GBMs. One blogger writes that CHAID is a better explanatory/exploratory tool, while CART is a better prediction tool: http://www.bzst.com/2006/10/classification-trees-cart-vs-cha...
Some other comparisons:
https://stats.stackexchange.com/a/61245/36229
https://stackoverflow.com/q/9979461/2954547
So the answer is that CART specifically isn't used everywhere. Recursive partitioning is used everywhere, mostly because it is simple.