Why are pandas/R/etc so common in a data scientist or analyst's workflow when one can resort to UDFs in an RDBMS?
I think the answer might be this:

The main difference between Python -and R- and SQL is that the first are Turing complete.

A given programming language is said to be Turing-complete if it can be shown that it is computationally equivalent to a Turing machine.

That is, any problem that can be solved on a Turing machine using a finite amount of resources (i.e., time and tape), can be solved with the other language using a finite amount of its resources.

Typically, one proves a given language is Turing-complete by providing a recipe for translating any given Turing machine program into an equivalent program in the language in question. Alternately, one can provide a translation scheme from another language, one that has already been proven to be Turing-complete.

Nearly every existing computer language is Turing-complete. About the only computer languages that aren't Turing-complete are a handful of special languages that are capable of LESS than a Turing machine - usually because some limitation is "hard-wired" into the language's structure or definition. (For example, Hofstadter's designed a language called BlooP so that it was impossible for it to have a iteration structure with an arbitrarily high upper bound.)

Turing Completeness definition

The question of yours is: Why we don't use SQL (or another DBMS) to do all the Data Science process? The answer is that because SQL lenguage is limited in certain aspects that Python and R are not. And one of those aspects is key to Data Science: Recursion.

Just imagine Decision Trees and all their variants without recursion! They are impossible!

Is SQL Turing Complete?