I agree, I don't know why mulberries aren't more popular.  They are delicious, and the trees grow much more easily than other fruit trees.  Other fruit trees seem very susceptible to fungi and insects, in my experience, but mulberries come up all over the place and thrive easily on their own (at least here in Missouri).  I have four mulberry trees in my yard that just came up on their own over the last 10 years, and now they are producing multiple gallons of berries each per season, which would probably translate into hundreds of dollars if you had to buy a similar amount of raspberries at the store.  

You can either spread a sheet to collect them, or if you have time to burn (or if you want a fun activity for your kids to do), you can pick them off the tree from the ground or from a step ladder.  My guess is, that is probably the biggest reason why people don't take advantage of mulberry trees more than they do:  how time-consuming it can be to collect them (but this is true for any delicate berry, and hence why a pint of raspberries at the supermarket costs $5). 

Edit:  also, if you look really closely at freshly-picked mulberries, most of them will have extremely tiny fruit fry larvae in them and crawling out of them, which becomes more noticeable after you rinse the berries.  This probably grosses some people out, but the fruit fly larvae are extremely small (like, barely perceptible even if you hold the berry right up to your naked eye) and are perfectly safe to eat.