For balance and discussion, Andrew Gelman's critical review of 'The Book of Why': https://statmodeling.stat.columbia.edu/2019/01/08/book-pearl...
I fall heavily on the Pearl side of this debate, because I'm interested in scaling to thousands to millions of variables, and though graphs are not a great tool, they are pretty much the only one that I think we have for scaling that direction.
That said, I think their disagreements don't have much effect on practice, and have as much to do with their different academic lineages as anything else. I expect that any dispute will be resolvable as the science progresses
Are you able to elaborate?! It'd be really interesting to hear what/if tooling exists for these graphs. I just found the book recently and am listening to the Audible version. It also reaffirms my desire for a "Bayesian inference" spreadsheet like tool. Something that'd help organize a few dozen thoughts ideas for researchers/engineers.