As far as I can tell, there are two mainstream conventions for defining formulas in FOL. Sometimes predicates of arity $0$ are allowed, thus countenancing propositional variables for FOL. Other conventions disallow propositional variables.
I’ve only ever had experience with the first convention, as I think it is much more standard for philosophers. However, mathematicians seem to be adamant that FOL doesn’t contain propositional variables. This is expressed here: Is there no propositional letter in first order logic?.
Is this just for the sake of defining a simpler system, or is there an actual reason to remove propositional variables from FOL? Is there a reason to remove predicates other than $\in$ from set theories? It seems to weaken our expressive capacities, even though adding propositional variables doesn’t do any harm. Further, this convention flies in the face of the “bottom-up” approach for defining new/more expressive logics/theories out of simpler ones. Is there an actual mathematical reason for this convention, or is it just standard practice?
It depends on what you are doing. For many uses of FOL, sentential variables would simply add clutter without providing any benefit.
For example, in model theory we have structures for FOLs. What would (for example) the first-order theory of groups look like with an addition sentential variable? What assertions about a group would the variable allow you to make? What would happen to the notion of elementary equivalence or elementary substructure? While it would not be hard to come up with answers, it would just be extra work with no payoff. It's a similar story with axiomatic set theory.
Typically definitions and proofs in logic use induction on the complexity of formulas. With sentential variables, you have an extra case to deal with, again with no applications.
In short, leaving sentential variables out of FOL doesn't actually "weaken our expressive capacities" (at least for the things one wants to express in model theory), and it does a (small) amount of harm, namely clutter.
Z.A.K. mentioned that in the proof-theory context, one does include sentential variables. I just checked the classic text Proof Theory by Schütte, and sure enough, his definition of what he calls CP (for "Classical Predicate" calculus) does include sentential variables, along with the sentential constant falsum ($\bot$). On the other hand, the text Proof Theory by Pohlers focusses on number theory, so he does not include them.
My knowledge of formal philosophy doesn't go much beyond Quine, so I don't know why philosophers would routinely include sentential variables. I am puzzled by your "Beauty is beautiful" example. What exactly do you gain by representing this with a single variable $B$? If you wanted to analyze the meaning of that statement, wouldn't you need something with more internal structure? How is having a sentential variable $B$ better than having an individual constant Beauty, a predicate symbol isBeautiful, and writing the formula isBeautiful(Beauty)?
But if it is indeed standard practice in philosophy, there must be good reasons for it.