This is just my theory.
Because it was the first tree based algorithm and Leo Brieman really did market it out. He even trademark Random Forest.
Kinda like how XGboost is doing right now.
My professor is also trying to market his version out too. If I get around finishing my thesis. His algorithm problem is that it isn't ported to any language at all. It's written years ago in a C and he's not a programmer.
I'd imagine it is the same with the other algorithms. Leo on the other hand is a CS major on top of a Stat major.
Also there are tons of regression algorithms out there that can be made into trees (their fully nonparametric counter part).
But in the end linear regression is the most popular next to logistic iirc. There's survival trees and BART bayesian trees which is in it's infancy.
- 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.