Is there are reason why they would take such a course of action?
I can not think of any other reason why European counsel would not like to follow your advice (I suppose you have given that advice) to file a Pre-Appeal Brief for Review, than they are basically unknown with that procedure. As a matter of fact, as European patent attorney with 20 years experience, also dealing with US prosecution, I have only become acquainted with this procedure last year, when one of the US patent attorneys that prosecuted our applications proposed to do that.
Apparently, but correct me if I am wrong, this procedure is not that common.
Further, if there would be a choice between filing an RCE and filing an appeal (or the pre-appeal brief) it seems safer to go for an RCE, since that is a known procedure. Filing an appeal seems only to be available as a last ressort.
Also, is it true that when the European Board of Appeals affirms the Examiner's final rejection, the applicant would need to file a European Divisional application to put the invention back into prosecution?
If a Board of Appeal affirms a final rejection, the application is definitively refused and can not be put any more into prosecution. The last chance to file a divisional application is to before the BoA gives its decision. However, with the current changed rules for filing divisionals, it is no longer possible to wait so long with filing a divisional: a divisional can be filed up to 2 years after the first Office Action from the Examiner, and generally when your file appears before the BoA, you have long passed that term.