Of course, it you're spending a little time in a place for what might be the only time there are probably one or two things you sorta have to see. But you should mostly avoid (IMO) just checking off sites.
The trap is, of course, that it's monumentally stupid to cram "seeing London" into the timeframe of one week. The bigger the city, the longer the time it takes to properly take it in. Otherwise your travel experience is a 200 km/h carousel ride: what can you even retain and process, at that speed?
What's the difference between seeing the Milan Dome in-person for a brief 20 minutes (because you have a laundry list of stuff to do) -- and seeing it in pictures? Not much, in my opinion.
Personally, I'd rather see only 1/5 of the "objectives" available to me, if the ones I DO end up visiting stay in my memory.
I know a number of people who travel rarely, as they can't often afford major trips. Their trips frequently include a relatively large number of must-do items, because they've spent a lot of time planning the three or five or seven days they can afford halfway around the world.
And this is before getting into what the obsessive planners I know do when on vacation!