Core decks vs extensive reading

Well, I think it's quite worthwhile to do Core 3k regardless of the rest of your study plan. That first 3k words is going to show up -constantly- know matter what kind of material you read. The core decks do come with example sentences (and audio for at least the early ones. At some point there isn't whole-sentence audio I think, I forget at what point.) So it's not like these are words completely without some example context being simply learned in a vacuum as a Japanese-English word pair. And it is of course, quite a bit easier to read when you don't have to look up every other word.

If you're comfortable doing graded readers, News Easy, Erin's Challenge https://www.erin.ne.jp/en/ , readings from chokochoko https://chokochoko.wordpress.com/the-great-library/ , and so on, then I wouldn't particularly recommend doing 6k/10k or whatever of the bigger sets.

One option to consider, however, is to download 10k, suspend all the cards, and unsuspend them as you encounter the words in your reading. That saves you the trouble of creating cards for any card that is in the Core 10k. Of course, you will still need to create custom cards for words outside of Core if you want to SRS them.

Edit:
Looking over your post again, it seems to me your question may be more 'should I SRS vocabulary or just read?' ... and to that the answer is -definitely- that you should SRS vocabulary. It's very easy to 'lose' vocabulary that you don't see for a little while when trying to 'just read' as a beginner, or even an intermediate student of Japanese (or any language). Many people will say 'but people learned languages without SRS for decades!' ... well, -sure- they did, but they didn't learn without vocabulary -flashcards-. And SRS is just a timing system to make it easier to spend -less- time on your flashcards. Which is why you should SRS your vocabulary rather than a) forgetting it or b) over-reviewing it with traditional flashcards.