Update ID field with client object model

I'm trying to create items in a list and set the ID field programmatically (for use in a lookupfield in another list). This works serverside by setting the property ReadOnlyField of the field ID to false while inserting.

Code:

private static void InsertItemWithID(int itemID) {
using (SPSite site = new SPSite(siteUrl)) {
    using (SPWeb web = site.OpenWeb()) {
        SPList list = web.Lists.TryGetList(listName);
        list.Fields[SPBuiltInFieldId.ID].ReadOnlyField = false;
        list.Update();

        SPListItem item = list.AddItem();
        item["Title"] = "This item Id's is not auto-generated by SharePoint, it explicitly specified";
        item[SPBuiltInFieldId.ID] = itemID;
        item.Update();
        list.Fields[SPBuiltInFieldId.ID].ReadOnlyField = true;
        list.Update();
    }
}

}

Now i'm trying to get this to work with the client object model - without success. Instead i'm getting the error message "This field cannot be updated.".

Here's my code:

private static void InsertItemWithSpecificIDCO(int itemID) {
ClientContext context = new ClientContext(siteUrl);
List list = context.Web.Lists.GetByTitle(listName);

var fields = list.Fields;
context.Load(fields);
context.ExecuteQuery();

var field = fields.GetByInternalNameOrTitle("ID");
field.ReadOnlyField = false;
field.Update();
context.Load(field);
context.ExecuteQuery();

ListItemCreationInformation itemCreateInfo = new ListItemCreationInformation();
ListItem newItem = list.AddItem(itemCreateInfo);

newItem["ID"] = itemID;
newItem["Title"] = "This item Id's is not auto-generated by SharePoint, it explicitly specified (Client Object Model)";
newItem.Update();
context.ExecuteQuery();  
}

`

Does anybody has a clue whats going wrong?