Dear Ulf,
"Bastards" have not always suffered scorn and derision throughout Christian history; nor can I see why they should have done. William the Conqueror did not have too many problems in asserting his right to inherit the Dukedom of Normandy, or attracting enough people to conquer England; or for illegitimate children of English Kings in the sevententh century (usually Dukes) to find eager matches. In Wales the legal rights of illegitimate children were almost the same as of legitimate ones. And in England, from the sixteenth to eighteenth centuries, it was quite normal for fathers to acknowledge and make provision for their illegitimate children in their wills.
I think I agree with you that except in some places at some times the illegitimacy rate in most traceable pedigrees is probably so low as to not make genealogy worthless - even in terms of genes. But the possibilty has always to be there.
The chances of illegitimacy vary radically between class and class, time and time, and place and place. And they are very different. Anne Boleyn, for example, lived in different apartments from Henry VIII; people in his court had reason to vist her saying they were bringing massages from him, therefore allegations against her may (or may not) be true. For the lower classes at the same time, the women had to go out to work, and equally had a possibility of a fling. But for quite high gentry the possibilities were very limited. The houses were crowded; they are small by todays's standards, even when they sound quite grand. There were lots of servants around.Etc etc
Mark