Good thoughts, 13umm!
As it happens, there are a number of clinical indices available to professionals that could be used in some of the ways you propose. Some of them use norm-referenced scales (from the WISC-V Integrated) that do address 3D spatial reasoning in a motor-free format. There are also subtests from other cognitive instruments (e.g., UNIT2, SB5) That include those types of tasks in their standard batteries. I would suspect they are not used more widely because having too many different measures in a highly-competitive (and often contentious) admissions process tends to create more opportunities for either gamesmanship or litigation--both of which also tend to increase inequity in admissions, since they generally are more accessible to highly-resourced families (not only those with more wealth, but those with more knowledge of educational institutions, and those with more social connections).
The more quantitative and objective reason they are not in wider use is that the published indices, on the whole, have stronger psychometric properties. One can put together many different combinations of subtests to create new proposed indices, but not all of them will be equally robust from a statistical standpoint.
On a practical level, the use of the Spatial Test Battery by Johns Hopkins University's CTY talent search program is exactly aimed at your concern about insufficient representation in standard IQ tests from visual spatial thinking skills.
Some of the other qualities (for example, different aspects of working memory) are not addressed on tests like the WISC because memory is not the primary focus of the test. It is only being sampled because of it's contribution to overall intelligence. There are other measures that are designed to look more comprehensively at aspects of memory (such as the WRAML-2). Those assessment instruments usually would come out only when indicated by specific concerns, and typically in the context of a much more comprehensive evaluation (such as a neuropsychological), extending beyond cognition.