Raymott! You said in two different opposite ways for "would imagine"
First, you said it's conditional mood, then later reinterated that opinion is related to other verbs like "imagine" not "would".
No, I didn't call it "conditional mood". As I said in post #16, “It might not be classified as a "conditional sentence" in traditional grammar, but it's not hard to imagine its origin in some form of conditionality.” This related to the examples I quoted.
My point here is that “I would imagine they’ll buy a new one” and “I imagine they’ll buy a new one” are both equally opinions, therefore it is difficult to see how ‘would’ makes it an opinion.
“Would” is commonly used when expressing opinions, wishes, etc. (“It’s true that ‘would’ is often associated with the expressions you’ve given.” post #18)
The fact that we say “I would like ...” more often than we say “I would hate ...” is not a sign that “would” makes an expression of desire. And the website doesn’t actually state that it is. It merely has headings “Opinion and Hope”, etc. with some sentences using “would” below. They then let you decide what they mean by that.
But the important thing is: Do you know how to use “I would imagine they will buy a new one”, etc? If you do, then whether there is any amount of conditionality implicit in the sentence is not important. (As you’ve seen from above, there is not agreement among native speakers, but understanding the technicalities is not necessary to understanding and using the phrase.)
Are other usages of "would" all related to "remoteness" instead of conditional? or are they all both? What is the exact meaning of remoteness? Is it the distance between the speaker and the listener or less chance or possibility of the event mentioned?
I wouldn’t teach “would” the way this site does. It doesn’t seem useful for me to be constrained by their terms and to explain what they mean – when I disagree with the implications they’re making, and in some cases, am not really sure what they mean.