I wouldn’t say it’s rushed. It looks very doable for me, from a logistics point of view. Of course, you’ve done something I don’t like to do…you’ve picked a number of countries to visit, and will only visit that country’s largest city (or one of its largest cities), with the exception of Brugges. But nonetheless, you picked great cities, and it’s doable, IMO.

Some of your commutes might take all day, so you may actually spend only 2 full days [rather than 3] in Berlin, but your itinerary has enough “cushion days” that it should be fine (you won’t be spending your entire time in train stations and airports).

If it means anything, you don’t really need to consider Versailles a “daytrip” from Paris. Versailles is a half-day trip, not a daytrip (I suggest going in the morning, be back in the afternoon). Today, Versailles is just a suburb of Paris, and you’ll take the RER (Paris metropolitan area’s suburban commuter rail) to get there. So, depending on how much you want to see and do, you can cut a full day out of Paris. (The day you fly in, are you counting that as one of your “4 days” in the city?) London too…if you only end up spending 3 full days instead of 4, you’ll be fine.