The philosopher's stone was a specific historical idea, the catalyst that would allow alchemists to create the elixir of life.
Imagine picking up a book called "John Smith and the Architect's Compass" and having someone tell you the title makes sense because there is a legend about an ancient cult who guards a a device that can locate the holy grail.
At the time she was an unknown author with a single kids book. I think changing the title to make the theme more obvious was justifiable. Changing the term throughout the book was unnecessary.
Personally, I grew up with the Philosopher's Stone and always wondered why she chose that name. It was only years later when I learned it was a legend outside the books did it make sense. The book does explain the meaning in the context of the novel, but not the wider cultural significance. That dampens the impact (just like how the Crystal Skull is not nearly as impactful as the Holy Grail in Indiana Jones).
Not sure why the title should be changed to sound like it has something to do with magic. For people who are aware of the legend, the original title would mostly bring up associations with alchemy.