Easy Solution here:
IEnumerable<tabitem> items = mainTab.Items.Cast<TabItem>().Where(x => !x.Name.Equals("welcomeTabItem"));
foreach (TabItem item in items.ToList())
mainTabs.Items.Remove(item);
First cast as IEnumerable<TabItem>, after that you do a Where query that excludes only the welcome tab. After you remove all the items from the TabControl.