HN being an obvious example, but there are plenty of others, each with its own approach.
Many successful online discussion forums rely on user moderation, which makes it feasible without Inquirer hiring a huge dedicated staff.
They have done.
Removing comments will reduce some engagement, but as pointed out they've come to the conclusion that the sort of engagement lost is of low value to the majority of their target audience and comes with a cost (in terms of moderation effort) that isn't worth, to them, any residual "good" value the comments sections have.
>HN being an obvious example
I think a key difference between HN and news pages like those in the enquirer in this matter is that their comments area is more of an afterthought to start with where much of the purpose of many visiting HN, good sub-reddits, and do forth is for the comments. This means removing them would be much more sufficient a loss. It also means that for a greater part community moderation works, reducing more costly (for the need site) central effort (it is still needed, of course but the cost/benefit balance is very different).
Also, a large part of it may be that the comments are at the bottom and a large part of their readership don't get that far on many articles. Some will read the headline & byline, some complete the opening paragraphs, and only then if it seems interesting enough (or they are otherwise lacking anything to do) will people read on further (never mind all the way to the end of a long article). Getting around that by putting the comments higher up probably isn't a good answer. I've seen some places have a "<number> comments below" link near the top but I can't imagine that drawing people through unless they would read that far anyway or the <number> is high enough to suggest some interesting controversy.