Are most of Europe's largest rivers too shallow to accommodate transport vessels?

Answer 1

The major rivers in Europe are all capable of taking transport vessels. Some can take larger ones than others, and the further upstream you go in any river, the more difficult it is. You question could depend on what you mean by "transport vessels" as that could be anything from small boats to cruise liners or tankers. Most cruise liners go to cities near coasts, so the rivers are deep enough there. Many of the major rivers also run river cruises which travel well up along the rivers.