Is there a rule-of-thumb best size for PSE catalogues?

Another reason not to split catalogs (except if they are totally unrelated to each other) is that it's extremely difficult to merge them in Elements if you change your mind (contrary to Lightroom).

My situation is a bit different from the one of Greg: I have 100K images catalog on a modest hardware setup, just above minimal system requirements. No speed issues even if going from 8 GB to 16 would be recommended. The speed issues are not related to the catalog, they come from my system, particularly for the backups. I don't use face recognition nor smart tags, auto creations, which would be crippled by splitting catalogs anyway.

If you are happy with the way the catalog is performing in the Organizer, there is absolutely no reason to split it up. 

I don't think it makes any sense to provide you with a rule of thumb.  You are going to have to decide what works for you.  I have a 200K catalog.  I also have a very fast computer.   It takes about 5 seconds to load the catalog from a warm launch.  Scrolling through the grid is smooth as silk.  So, I see no benefit to break up my catalog.  That would only hinder me.

If you are finding that performance is slow with a 55,000 file catalog, I can't imagine that you will see much improvement splitting your files into two or three collections.  It should be easy to test this out.  Simply create a new catalog with 25,000 files and see if it makes any difference to your experience. 

The photos have come from earlier systems running Windows 7 and its predecessors, and many were previously catalogued on those laptops with PSE 9 and earlier versions. I have eliminated all or most of the duplicates. I also have saved the keyword tags on all that were catalogued and I have tested and find they are imported successfully into a test catalogue.)

By @sylvia1152

The fact that your catalog was created with earlier versions should make no difference whatsoever to any performance issues.