It might help to understand that a systematic review is not a mathematical or algorithmic procedure with a precise and perfect result. That is, even though the goal is that two different review teams should reach the same results, because a systematic review is a complex social process, it is impossible for two independent teams to arrive at exactly the same result, no matter how systematic they are. For example, even if both teams follow exactly identical processes (which is practically impossible), but one team searches in December 2021 and the other team searches in January 2022, the results would not be identical.
If you come to terms with this reality, then you should be able to accept that the goal of a systematic review is not to be perfectly reproducible but to be as reproducible as is reasonably expected by scholars who do high-quality professional work.
Regarding the selection of databases, it is reasonable to limit your search to the best-known and most widely used scholarly databases for the specific discipline or disciplines that fall within the scope of the review. These can be determined by reading past reviews from the relevant disciplines and being sure to at least include all the databases that these have used. (Of course, your own review team might not have access to all the databases that you find in the literature, so this might not be feasible.) If two separate review projects strive for that standard, even if they do not use identical databases, I estimate that they should have 95% or greater overlap in studies that they locate. (The greatest disparity would be with grey literature. For example, if both teams search Google Scholar and get 200,000 results on the keyword search, if both teams are maniacally meticulous, one team might look up only 500 results whereas the other might look up 1000, so results would not be identical.)
However, if both teams target the same databases that are known by the discipline as the most comprehensive, most of the highest quality peer-reviewed results should be found in both teams' searches. The main differences should be in work that is published in dates between the two searches, including grey literature.
So, in brief:
- There is no truly non-arbitrary way to choose literature databases. There will always be arbitrary choices made.
- Professional quality means doing your best by following past precedent to include the databases that are widely acknowledged to be the most relevant for the discipline.
- Systematicity does not mean being perfectly reproducible, which is impossible--if that is what it meant, then no one is "systematic". It means being professional to be as systematic as can be reasonably expected.
One more thing: a closely related theme to systematicity is transparency, which means being explicit to report all procedures. This is important because, given that perfect systematicity is impossible, transparency allows future researchers to better understand why their different choices might result in slightly different results from yours.