The advantage of the "4-joint base" as you call it is that it gives you Noga setup ease, without the price. It's easy to swing your indicator to the solid half of the arm when you need a stiffer connection (which you will often want to do, as that elbow does have quite a bit of lspring to it).
For my part, I've used a lot of bases, and the HF base is just as good as any other coming out of China at 4x the price. And if you have such a base, I suggest you pick up a $10 indicator to go with it anyway. That way, you have something to lend to someone. Because while I am particularly free with lending tools, certain things absolutely positively never get lent out. Dial indicators (and calipers) not made in China, chainsaws, my SpeedGlas, and any torque wrenches not from HF.
And that $10 indicator gets used from time to time. That's what I've got on my tire balancer, that tells me if a rim has an unacceptable amount of runout (or isn't mounted correctly on the balancer). It's also sufficient for checking parallelism between my tablesaw blade, slots and fence. And every time I use it, means less wear and tear on the good ones. But when I'm centering a part in a 4-jaw chuck, you can be damned sure I'm using a real gauge. I've got a box of indicators from Federal, Ames and Starrett for that work.
As you said, just about any tinker toy gauge will read to .001", but to actually trust it to be accurate to that level is another story.
+1 Again, that's my biggest argument for owning a cheap indicator too. Hide the good one.