About the only real reason I could see for running the coax inside the mast would be if you're in a suburban environment, and you have an Earth-first greenie whacko for a neighbor who thinks he's doing "mother earth" a favor by destroying a radio transmitter, or some know-nothing who blames every pixelized tv picture on your big bad "CB" radio.
In those cases the whackjobs favorite method of attack is to pin (or cut) the coax.
Since electrifying your tower with a neon sign transformer is probably illegal at worst and detrimental to your signal at best, and most suburban and city ordinances frown uipon barbed wire obstacles around your tower, you may want to secure the coax as best as you can so that there's no weight issue and then run the coax into the ground through some good thick electrical conduit and then into your shack.
Of course, this only really applies if you're concerned about some schmuck trying to destroy the fruit of your hard work and interefere with the enjoyment of your hobby.
Of course, I'm only ranting about things I've heard in the past-this is in no way an endorsement of nor a condemnation of any one (sane) person or group of (sane) people.
A note on zip ties-use 'em sparingly. As others have said, if you pull them too tight, they *will* damage the shielding of your coax, sometimes right away and sometimes with time.