FTDNA note - if you don't want to mess with just a few matches at a time in the chromosome browser, you can run a report (near the top right of the screen) which will give you all of your matches at once.
Download All Matches to Excel (CSV Format)
23andMe note - one thing that makes them nice is what's called FIA. This is a utility that allows you to see how your matches match one another. FTDNA lets you see that your matches are related, but not where. 23andMe's version of the chromosome browser (FIA) allows you to compare your matches against one another which can be really helpful. I'd love to see that functionality here.
Yes, you are correct in that I have many colonial ancestors. As a result, my parents have many common (distant) matches which can be very messy when you can't see which chromosome they match on. I have a number of people with whom I share different segments from each of my parents. The shakey leaf doesn't address that well.
As a side note - I recently found someone who matches both of my parents, I inherited those matching segments, and my husband also has matching segments from this person. Can't imagine what that might look like for my kids. I guess I'll just have to hope they have created better ways to compare chromosomes in the future.