While I assumed that the problem was with the Word styles used, I also would have thought that Trados would have had a fix by now.
There is a very simple fix: simply make sure that the source document is properly formatted - if you get a document with differing formatting settings (typically, user changing the font to Arial by way of character formatting, oblivious to the fact that the Standard style is set to Times New Roman.
Note that the behaviour of reverting back to the font that's determined by the style used isn't a Trados-only issue - this can also happen when merging paragraphs, for example. Once again, this is a Word issue (although not a Word fault).
Your post seems to suggest that there is a fair amount of manual repair involved, whether fixing the source document styles at the beginning or the target document formatting at the end of the job.
The amount of work depends on the variety of styles used in the document - I cannot recall having spent more than half an hour on this in each case. What's much worse is when Word 'users' use tab stops and carriage returns to 'format' paragraphs...
Is there not a way to tell Trados to preserve the style settings of the source document (however irregular they may be)?
But that's exactly what Trados does...
It seems like with Western European languages it would be highly possible to turn off whatever automatic setting it is that changes the style settings in the source documents to something different in the target document.
Once again: Trados does not change any style setting - you could say that it enforces them on badly-formatted Word documents.
This issue is one of the reasons why Trados are considering adapting TagEditor to handle Word files, too (see this thread) - but then, not everyone would be happy about that, either. Go figure...