I imagine most people today do not even know what "begotten" means. It is not a word commonly used today.
However, everyone knows what a "son" is... it is the child of a father.
To say that Jesus is God's one and only son, is the same thing as saying he is his "only begotten" son, in today's vernacular.
I've never heard anyone argue about that. Ever. Well, except for the KJV onlyists, who want to insist on using archaic words and phrases that MOST people don't understand anymore.
The idea, or thought, or fact that the word is getting across STILL comes across, accurately.... in language that people can understand.