Thank you Dmitri and Sean!
I'll sure use the default page template filters later on.
But, my problem was that I found out that only for the 'Home' Page Type, the features 'Page Builder', 'URI' and 'Navigation' were enabled. I've selected these three features for another page type 'ABC' and all the Default page templates that were showing to 'Home' page type started to show also on this 'ABC'.
Was that really the reason ? So to be able to select a Default page template, the page type has to have these features enabled ?
Thank you very much !