Flashings are typically metal and prevent water entry at gaps where the building is likely to have penetrations. Over time, and sometimes due to poor installation, flashing fail. This will sometimes allow water into your home into an area not accessed very often therefore it can go undetected from days to years.
The answer is water shedding like an umbrella. Water can and does enter your house at various points like under shingles with wind driven rain and deficient flashings
Typically time will take it's toll on the flashing, especially with this Houston humidity. Alternatively, the fasteners(nails, etc) can fail(wrong type, not sealed correctly) and it can allow water to penetrate. Also mechanical damage is a possibility - a vehicle, someone careless with a ladder, an accident, dogs, etc
Short answer, NO. Caulking is used in a variety of ways in construction, from sealing windows, to plumbing, even to help seal flashings. Caulking is only designed to last a few years, although it's been my experience that it lasts far shorter then that. The average home owner will not remember to climb up on their roof every 18 months and recaulk everything thats worn out and eventually the caulk will dry out in the heat and crack.