I had a pair of lace-up shoes once, and even though I had tucked the laces into the shoe, they came out and got caught in between the chain and chainring. That resulted in pulling the lace until my shoe was extremely tight, and ripping the lace to shreds. Now I won't ride a pair of lace-up shoes unless they have a velcro strap or cover for the laces.
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It's like riding a bicycle