No …
I’ve never been great at writing letters (which might sound weird, given I write blog posts …). So no, I don’t write to authors if I love a book. On the other hand, I also don’t write to author if I don’t like their book.
It’s one thing to interrupt an author’s real or virtual mailbox with a compliment. It’s something else to invade their privacy with an unsolicited rant detailing everything wrong with their book.
I do offer manuscript assessments as an editing service, but that’s different. With a manuscript assessment, an author has specifically engaged me and paid me to read and critique their book. Even then, I aim to give specific feedback and offer solutions, not deliver a detailed rant.
But kind of …
I do write book reviews.
Authors sometimes approach me and ask me to review their book. If so, I do send them an email with a link to my review. Does that count as writing to them? I don’t think so.
However, I consider book reviews to be writing to readers (or potential readers), not to authors. I know some authors read their reviews, but I’m not writing to them or for them. I’m writing to and for readers.
But I will write a glowing review if I love a book. I will recommend the book and author to other readers. I may even mention the author when I post my review on social media. That alerts them to my review, but it’s not specifically writing to them.