Baylor, you will get yourself in difficulties if you commit yourself to the equation "good" = "influential." Lyly's euphuism was influential (for a time). Was it
good? It certainly was fashionable for a time.
https://en.wikipedia.org/wiki/Euphuism
So I'm going to dismiss "influential" as a criterion of goodness or literary excellence, at least till you or someone else makes an argument for that.
Second, you say Lovecraft has "entered the realm of classic literature," ergo he is decidedly a good writer. But what do you mean here? You are thinking that Lovecraft is represented in the Penguin Classics and the Library of America, I suppose. It is at least a possibility, though, that the editors have introduced Lovecraft for motives of gain, or that their judgment was in error. I mean, editors have been motivated by gain and have erred in judgment, isn't it so?
I'm trying to push HPL admirers to make a case or cases for Lovecraft as a good author by stating criteria for literary goodness against which HPL has written some things that measure up, or in other ways to
try a little harder to do the work of making an argument(s) for HPL.
Putting the task this way will require you, or others, to get down to specifics, which (in my opinion) tends to be a real failing on the part of many Lovecraft advocates. They may assert his literary excellence as if his work is all of a piece, all good, except maybe for "Herbert West"! Such discussions aren't likely to convince those not already in love with Lovecraft.
As some who've read things I've posted may have divined, I've been wrestling with Lovecraft's literary attainment for years. I think I'vce recommended, for example, sincere attempts at thought experiments -- for example, suppose you did not know "Pickman's Model" was by your beloved HPL and you read it today. I've urged that serious readers attempt to read his writings without special pleading, without the aura of pleasure that I too feel in settling down once again with this author who captivated me at age 15.
These days I want to urge strongly that he could have been a developing writer who turned out a fair bit of low-quality writing, and some rubbish, and also achieved some outstanding imaginative work -- and seemed to be headed in promising directions in his last years.
A few months ago I floated a draft of a case for Lovecraft.
https://www.sffchronicles.com/threads/551838/
If it's been a while since folks have looked at the earlier entries on this thread (Is Lovecraft a Good Writer?), maybe they could be reviewed -- ?