I used to live in Seattle, and I went to Pike Place Market every chance I could just to watch, laugh at the fishmongers, have a nice lunch, window shop, and even sometimes buy something. It was better in the off season, still crowded, but not overly so. I tend to differentiate between sites that are crowded but worthwhile and actual "traps". For example, the Colosseum is worth seeing for its historical value; South of the Border is a Tourist Trap--fun to see, but built to make money and not worth braving huge crowds or making an extra trip. So is something like the London Dungeon--super fun, based on local history, but not about being an actual Londoner. Crowded but worthwhile sites are ones I will brave, but with some planning to minimise crowds.
The top sites are crowded for a reason, and if your goal is to see them, then do so. Doing it intelligently will help you avoid the crowds. People don't come to Europe from the US (or elsewhere) simply to sit on a beach exactly like the one in Florida. They come to see things they can't see elsewhere. The Colosseum is no less a real, historical place worth seeing simply because other people agree with the assessment that it is worth seeing. It's still a marvel to see its complexity, to consider its history, to get a sense of what it might have looked like back in the day. Though of course, you may prefer to visit El Jem in Tunisia--the same thing, slightly smaller, FAR less crowded, and you are able to walk around more freely and get a better sense.
So that's my take on "sites" or famous locations. But when it comes to seeing how people live, what life in a place is like, or seeing something different from home that is unexpected (let's face it, when you visit Rome you tend to know exactly what you will get), you have to get off the beaten track and, more importantly, be OPEN to it. That means NOT having a tight itinerary or a list of must-sees. It means having only a rough plan, trying something uncomfortable or unusual. It might even mean missing the "preferred" sites in favour of places that are less known. Heck, Rick started his whole business on this model.
I live in Hamburg. Our tourists are almost exclusively other Germans (mostly for the musicals) or cruise ship passengers. Those of us who live in Germany and are familiar with the north have posted countless attractions and locations that are authentic simply because they have not been overrun by foreign tourists. Yet I have yet to see more than a handful--meaning maybe 5--who have never lived in Germany post about visiting virtually any of the places outside of the city of Hamburg. Those who were stationed in Germany or live here now seem to be the only ones who visit places like Glückstadt, St. Peter-Ording, Glücksburg, Greetsiel, or Aurich.
People want to see Nyhavn in Copenhagen for its picturesque waterfront, but a slightly smaller, very similar waterfront (also built by the same Danish king) with NO crowds or endless tchotchkes shops exists in Glückstadt. It also boasts a cobblestone square complete with candelabra, a brick city hall, alleys with half-timbered homes dating back several hundred years, a weekly market, a Lutheran church also several hundred years old, museums, a small palace, a Jewish cemetery, parks, canals, and all of it on a beautiful dike with sheep and wind and seagulls. I have repeatedly mentioned it on this site and others, yet people insist on visiting places like Rothenburg odT instead. Why? Anybody's guess, but it is often FOMO, checklists, and wanting to stay in their comfort zones (people in RodT speak English, shops and menus are familiar, the town caters to tourists, and you know what you will see). But if they are pleased with the choice, who am I to tell them it's wrong? It absolutely isn't!