No, Trump as a person is not the problem; Europe has its own share of strangely acting populists. Rather, the image of US politics in Europe is deep down in the cellar because of news like the Snowden revelations. We get the impression that presidents have immense personal power but are not "in charge". In the end, the USA may blow up the world and nobody be responsible.

The risk is much smaller in systems where leaders are more embedded in their parties and parliamentary factions. See the recent events in Australia.