All good advice and as you probably know from my various review articles on printers and papers why I routinely use the i1Pro2 and a spreadsheet for results evaluation of the print pipeline. But of course not everyone is equipped with the kind of gear to do this, so at least visual side by side inspection helps to see the most egregious variances.
The two most important limitations of this approach with the ColorChecker is that its maximum Black is only about L*20, so evaluating the B&W luminance range from say 1~20 needs a separate set of patches, easy enough to construct in Photoshop, but here the visual evaluation of the deep quarter-tones can be really tough, so an area where measurement is all the more useful. The other limitation in respect of the colours in the GMCC is that their gamut doesn't really challenge our latest generation of gloss/luster papers, inks and printers. One needs another kind of target to challenge the limits of these materials and equipment. At the same time, one wants to be careful not to print much for testing that is out of gamut, because that introduces the whole business of how OOG colours (and in Perceptual Intent, others) get shifted, which is not normally the purpose of these tests.
Finally, a "mental factor" - one shouldn't get hung up on small variances that for most intents and purposes one wouldn't perceive on a stand-alone basis in a normal photographic print. There are tolerances, unless one requires pretty close accuracy for special purposes.