Interesting question. The warranty that comes with the Mac is one year, so you are certainly covered for that period, although AppleCare+ does add the two accidental damage claims per year (albeit with what some might consider pricey deductibles), so that's a thought.
Also, there seems to be some debate as to how long after the purchase you can buy it - some of it based on country, and some based on...I dunno, the whim of Apple? 60 days seems to be the norm, but I'm also seeing reports of up to a year. Clearly some knowledgeable guidance from an Apple rep is required.
(Plus now, a renewable year-to-year Plan).
As you note, Apple's own website of the Plan says '...AppleCare+ for Mac extends your coverage from your AppleCare+ purchase date...', so you are extending the warranty to, essentially, 3 years and 60 days from date of your Mac purchase - but again, those 60 days won't be covered by the 'accidental damage' claim. If you anticipate your Mac primarily sitting on a desk, and no liquids allowed nearby for the first 60 days, then that shouldn't be an issue.
And after the initial shock of paying for a Mac, I can well understand perhaps holding off on AppleCare to allow your bank account to recover a bit.
Comes down to your comfort level, I think.