What is a real-world use-case/need for a left-recursive grammar?

I understand the basics of how left-recursion works, and why some people say it's bad. And I've also ready opinions such as:

...like LL and LR parsing, PEGs are often frustrating to use in practise. This is, principally, because they don't support left recursion.

http://tratt.net/laurie/blog/entries/parsing_the_solved_problem_that_isnt

But this leaves me confused.

I haven't read about an actual real-world use case of why you'd even need left-recursion in the first place, especially if there are techniques to convert left recursion to right recursion. In addition, left-recursion feels less intuitive than right-recursion.

What is a real-world use case or need for a left recursive grammar to help me better understand? By "real world" I'm looking for an example grammar that is more human readable than the typical theoretical examples such as:

$A \to B\alpha \mid C$

$B \to A\beta \mid D$

For example:

$filePath \to pathSegment*$

$pathSegment \to pathSegment \mid slash$

$slash \to /$

Part of the reason I ask is b/c left-recursion doesn't seem very intuitive; it seems more intuitive to use right-recursion. And also because I wonder if it's even a practical problem to try to solve.

Update

This makes sense, but seems to be the only major reason:

$E \to E - n \mid n$

converted becomes

$E \to nT*$

$T \to - n$

"10 - 5 - 3" is then parsed:

L-recursive : (((10) - 5) - 3)

R-recusive : (10 (- 5 (- 3)))

http://etymon.blogspot.com/2006/09/why-i-prefer-lalr-parsers.html

Is that all?