"New Vehicle Limited Warranty", most definitely covers rattles as I have had my A/B Pillars and Pano Roof serviced or replaced several times... either I complained or Tesla proactively serviced or replaced...
Altho it should be fairly obvious that "consumables" are not covered... but having said that... I would have considered the 12volt lead acid battery to be "consumable" as well... but they also replace that free of charge while under "New Vehicle Limited Warranty". This is one of those things they do not replace for free under the "Extended Warranty"
Here is the New Vehicle Limited Warranty document:
https://www.tesla.com/sites/default/files/downloads/tesla-new-vehicle-limited-warranty-en.pdf
Pages #7 and #8: "In addition to the above exclusions and limitations, this New Vehicle Limited Warranty does NOT cover ... General appearance or normal noises and vibrations, including, but not limited to, brake squeal, general knocks, creaks, rattles, and wind and road vibration for which there are no malfunctioning parts requiring replacement ...Minor adjustments, including addition of sealant, insulation, or replacing and/or re-torquing of nuts and bolts (or the like)".
The wording in the 4 year ESA is similar: "The following components and defects are not insured by ESA: ... Adjustments necessary to correct all kinds of sounds, water leaks or wind noise".
Tesla may choose to address your rattles, but they don't have to (either under NVLW or ESA).
I think the 12v lead acid battery was covered because it was defective and died prematurely. They had a well publicised issue with those batteries, and the typical lifetime is 4 years (so failing after 1 year is a clear defect).
I am hearing a lot of FUD (Fear, Uncertainty, and Doubt) about the ESA (and have been hearing this for 8 years now, even back to the roadster days). It seems Tesla HK don't want to sell it, and have now taken it away (so it is not even offered at the moment). Given that I doubt even the 17" CID will last 8 years, I consider the plan worthwhile (and would have bought it just to cover that one component).