Why do some publication venues prefer TIFF over some vector formats?
Most figure file formats are acceptable, although TIFF is preferable.
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TIFF is the preferred pixel format for print due to being able to use CMYK (the colour format relevant to printing) and being lossless in typical use (using lossy compression cannot happen without clear intention in most programs). Moreover, this was already the case long ago, when formats such as PNG and PDF were only beginning to emerge or not even created and creating a good vector graphics was not feasible for your average scientist.
On the other hand, today where online publication is standard and graphics software has advanced a lot, TIFFs cannot really compete with vector graphics for most applications. Either the TIFF is of good quality, but then its usually huge, which is not desirable for online dissemination. Or the TIFF is reasonably sized but rasterisation shows. Moreover, almost all problems in vector graphics can be easily repaired by the production department, whereas repairing pixel graphics can be much more cumbersome. There are some exceptions where a TIFF is the best choice but even this requires, e.g., that the authors and their programs are CMYK-aware to gain an advantage over formats such as PNG.
So, I cannot imagine that any reasonable production department would prefer over TIFFs over vector formats in most cases, let alone allow TIFF as the only format. Thus, the reason, why the journal is preferring or requesting TIFFs is probably is probably one of the following or somewhere in between:
Note that the specifications you linked seem pretty reasonable to me at first glance and also marks EPS as a preferred format alongside TIFF. Moreover, it mentions embedding fonts, which only makes sense for embedding text as a vector object, which is not possible with the TIFF format at all.
TIFF is an image file with all elements of the image in a fixed position relative to one another(assuming layers are flattened). As such, it is easy to ensure consistency regardless of differences between the software used to create and display.
With files where the elements are separate, there can be alignment and compatibility issues if a file is opened in a different piece of software. A very clear example of this can be found with written documents. A .docx file opened in Microsoft Word, Apple's Pages, or LibreOffice, even something like a two-page essay with minimal formatting, can look quite different in each of these applications.
When compared to JPG, TIFF is a much higher quality format. JPG compression greatly reduces the quality of text and blurs hard edges between solid colours that are not exactly horizontal or vertical.