I guess I'd rather it show discontinued on their site, than them continuing to take backorders, or keeping an actually-discontinued item on their site for years.
As soon as we realized some of this stuff was not coming in any time soon, we stopped talking backorders and went to a call list model.
I know another company that has several items on their site that they haven't carried since 2016 or before. I am reminded of this when someone calls asking if I will price match a competitor's price (in general, we have the lowest price anywhere on most of our stock, but I will often price match if I do not, and it isn't a going-out-of-business/factory seconds/bent-and-dent scenario).
As soon as they tell me the items, I know which competitor they are talking about, and vice versa. One site in particular discontinued a certain item in 2012. From 2014 to 2018 we were the only company in the country that carried this item. People wanted us to honor a fairly old price from the days when every company in America still carried this thing.
Another no-longer-competitor hasn't updated his page since the first Obama administration, the security certificate for the website expired maybe six years ago, and the associated phone number and e-mail are dead. You have to go hundreds of pages deep into Google to even find the site, and when you find it it looks like a Geocities or Myspace page from the early 2000s. Still, people will want a price match with a company that is basically a curious artifact.