Flags do not last long at sea, and it is rare to find a merchant ship of any type in the open ocean flying flags. If we saw a warship or another company ship coming along, we would maybe put an ensign up so we could dip it in going past, or sometimes you may see an ensign up on Sundays in calm weather. For the most of the time, there was nothing. It was only in port that flags were put up, ensigns and courtesy flags, Blue Peters etc.
As for sailing ships being top heavy, most of them were not. You could say that galleons and ships like the Mary Rose and Vasa were not as stable as they might have been. Merchant sailing ships were not long and thin as is usually supposed, they had massive hulls with beam/length ratios often also low as 5:1, and had an awful lot of hull under water like this cross section of a big steel windjammer shows – look at the load water line on the right hand side. If the hull was 3,000 tons, and the masts and spars weighed a couple of hundred tons, why should they be top heavy?
Bob