I didn't learn English by reading vocabulary lists or dictionaries. Pretty much all was learned by context.
If you were to just listen to all the same input, you would never have learned anything. The learning comes from deciphering the connection between the reality you see and the words you hear.
And if you want to understand a document, which is just a sequence of unsupported words, it is equally true that you must already understand almost all of those words.
The point of learning by generic word frequency is to optimize study, not to attempt to brute-force understanding. If you have a document in front of you, would you rather have to look up every word in a dictionary, or only every other word?
I've been in this situation. There's no real difference between the two circumstances you describe.
--- 1 ---
Say you are presented with a politician's speech on some topic, topic X. Your background vocabulary is such that, out of the unique lemmas present in the speech, you know about 7/8 of them.
Without a dictionary, you aren't that likely to be able to answer basic questions like "is this politician for, or against, topic X?". With a dictionary, this will improve.
--- 2 ---
If you need a dictionary for every word in a document, that means you don't know any of the grammar of that language, and regardless of how much dictionary access you have, you're not going to be able to understand the document.
--- 3 ---
If we're glossing over grammatical particles, and you're allowed to use a dictionary, then this is a question of speed. The differences aren't as significant as you seem to think. A major reason for this is that words get repeated; if you need to look up a previously unknown word the first time you encounter it, you probably don't need to look it up the third time. Your reading speed will start slow and increase very rapidly, as long as you keep reading about the same kinds of things (for example, because you're reading a single document).
Put another way, the process of starting to read a document will convert you from a stylized "every other word" to a stylized "every tenth word" within a short time.
Why? Having spent a good amount of time living in Shanghai, I found it important to be able to understand menus. But there's no pressure to know the words for supermarket items; you can just go to the supermarket and look for the item.
Otherwise your point is correct; all semantic words are equally difficult and which ones you know depends on the things you like to talk about. Grammatical words are more difficult, and more important, but this is so widely understood that language-learning material already treats them as an entirely separate class of things to learn.
> Also, while it's easy to calculate word frequencies for stuff like newspaper articles, there aren't any good statistics (last I checked) around just normal everyday conversation. Because that stuff isn't getting recorded and transcribed.
(1) You seem to want COCA, which includes a bunch of transcribed telephone calls.
(2) Word frequencies are still the wrong concept. If you want to understand a particular document, you need to understand almost all of the words that appear in that document. (You'll be able to learn some of them from their use in the document.) If you decide to learn a list of "frequent" words, you're unlikely to be able to understand more than a couple of isolated sentences in any given document.