Is Lovecraft's work defined by his racism and xenophobia, or by his world building and Cthulhu mythos? Which of these two things is it you think people take inspiration from?
There are a whole lot of authors that have problematic views, but does that mean we must discard all their work? Can we not cherrypick what we do like when looking for inspiration?
Disclaimer - I'm the one who has repeatedly mentioned his children when talking about Lovecraft. I've done so very deliberately since, at least by two separate posters in these threads, I've been accused of fabricating the issue. That I couldn't possibly be directly affected by this sort of thing, thus, I'm only doing it to make myself feel good. Since, that's not true, and that I am directly affected by issues like this, perhaps I can now comment without having to justify myself to those who would turn these conversations into merry go rounds.
Disclaimer
No, of course not. And, let's be 100% clear here. NO ONE is suggesting that Lovecraft be banned or anything like that. Like you say, his works are an important part of the history of the genre, and, anyone who is interested in the history of the genre should read them. (Even if personally it makes me want to wash my eyes out with bleach every time I've done so) There are no calls for censorship here. No one is advocating "discarding" anything.
Now, what is being discussed is a list of inspirational reading in the Players Handbook of the Dungeons and Dragons game. This is not an academic paper. It is not a historical paper either. It's simply a reading list of suggested authors for DM's and Players to read to get ideas on how to have a great game of D&D. Lord of the Rings, Frietz Leiber, Elizabeth Bear and many others. And, frankly, most of the authors on the list are perfectly fine and can be included without objection. However, yes, Lovecraft is on this list. Without context or commentary. He's held up as equal to all these other fantastic authors which fill the fantasy genre.
I'm not sure that removing his name would greatly reduce the inspiration new players could get from reading these works. I mean, if you actually read all the authors on the list, except for Lovecraft, you'd have a very strong grounding in the genre. You'd have hit the high points, including Mythos stories, without having to get smacked in the face with authors telling you that you or your children or your spouse, or someone you know, is an abomination of nature that should have been strangled at birth.
Are we actually losing anything inspirational by removing Lovecraft's name from the list of Inspirational Reading in the Dungeons and Dragons Game? I don't believe that we are. I think we gain far more than we lose. This isn't about removing Lovecraft from the canon of genre works. Of course he has a place there. You cannot seriously be a scholar of fantasy genre without reading Lovecraft. But, this list isn't about making people into fantasy genre scholars. It's about readings that will inspire your game. Not referencing Lovecraft, IMO, will not result in poorer games, and might just make it a tiny bit easier to introduce the game to people.
