The DNA in Dublin shows otherwise ~ not that Brian Boru didn’t win a fight or two, but all the Vikings didn’t leave. Else Ireland would have had no cities and ports.
You are partly correct. The cities of Dublin, Waterford, Wexford, Limerick and Cork were original Viking settlements. The first recorded raid by Vikings in Ireland occured in 795 and for the next 200+ years they occupied parts of Ireland and did in some cases assimilate with the Irish. It is actually a fascinating period in Ireland. After 200 years of conflict, Brian Boru united the Irish for a final battle that virtually ended the Viking age in Ireland in the year of 1014.