Yep, these problems have been known about and acknowledged as biases in molecular methods for a few decades now.
Yep.
Copy number is not a problem unless if you really care about precise cell count. Even then,
- 16S copy numbers usually only vary slightly between species and multiple copies within a cell don't have major sequence heterogeneity (unlike, say, ITS, where it is a serious issue).
- Copy number can be corrected for some extent when it is known, and there are some software tools out there to do this. This is of course limited by whether that species' genome has been sequenced but this is a problem that becomes smaller each day.
- Copy number will not really impact beta diversity comparisons (small effect, applied evenly across samples)
Primer bias can be partially addressed by using degenerate primers. Still not perfect, but it works.
Amplicon sequencing can be quite precise when controlled properly. E.g., check out this paper.
There are other problems with that pre-print, e.g., it is based on a very small sample size (two mock communities?) which probably says more about the quality of the test data than it does about the methodology in general.
So yes, these are issues, no, amplicon sequencing is not perfect, but no method ever is and biology is messy. We're getting better every day. 