For the record, practically all my shoes these days are slip-on’s (easier for showings and repeatedly taking them off and putting them back on).
However . . . as someone who’s heard that line, ahem, more than once in their life, I thought — 
as a public service on behalf of non-shoelace tie’ers everywhere — I’d post the following rebuttal:
“Actually, no you won’t (trip on your laces if you leave them untied, that is).
I suppose if the laces are 2′ feet long, and the wearer is a small child whose stride is quite short, that’s a possibility.
But if you’re an adult, it simply won’t happen.
That doesn’t mean there aren’t valid reasons for tying your laces.
In fact, I can think of two: 1) so your shoelaces don’t get wet and dirty, especially if it’s raining; and 2) so you don’t have busybody strangers come up to you, point out your untied laces, and say, “you know, you’re going to trip on those!”
So there!
Maybe “Myth Busters” can do an episode verifying my insight (which I already know to be true empirically).
P.S.: In 1877, photographer Eadward Muybridge’s pioneering work settled a raging question of an earlier era: whether all four of a horse’s hooves are off the ground simultaneously during a trot (they are).
And yes, subways and escalators pose different threats to non-lace tiers.
