Well, yes, they do in some cases.
I tend to observe the following: Americans coming to Europe on business have a tendency to dress very well for their appointments as they would when going to the office at home, but while they travel and as soon as they have some "free time", they have a tendency to overdo on the word "casual wear". Shirts seem not to find their ways into pants and sneakers pop up everywhere. A word of advice: if you are over 25, please, no matter how sporty you are, leave the sneakers at home. There are very comfortable shoes on the market...
As for the tourists, the way they dress has nothing to do with casual wear any more. But here again, there are two groups: The wealthy or well to do who overdress on every occasion: you meet them mostly at the Georges V in Paris, the Excelsior in Rome etc. Then you have the run of the mill tourist... There I agree with you... sloppiness galore. Ghastly.