Another Elite Strap/battery owner here. You really need this, and honestly - it should be included as the default (without battery, - fine). The basic strap is just awful. Awful to adjust, awful to wear, - it's bad.
It's also a real shame how much worse value the Quest 3 is versus Quest 2. Quest 2 was so much cheaper, came with the silicone optional face piece (now $40), and the Elite Strap/Battery + Case was $130 for the combo pack. Now the Elite Strap/battery is $130, and the case is another $70. The dock is $130 and doesn't come with a power adapter. Meta recommends you use the 18W power adapter that came with the Quest 3, but then it's still not as fast as the ALSO recommended 45W adapter most users won't have - to charge the headset and controllers.
And don't get me started on the whole $150 to add an extra 384GB. The Quest 3 is unquestionably better than Quest 2 in pretty much every performant way. Value-wise, it's so much worse that it's no longer as easy a recommendation.