A pad abort launch escape system needs to get the crew clear of an exploding rocket and high enough for the chutes to open. Fast opening ballistic parachutes mean you don't have to get as high as in the old days, but an exploding rocket the size of a Delta IV Heavy or Atlas V Heavy still makes for a really big bang. It's best not to be anywhere in the neighborhood if that happens.

There's another problem: a catapault imparts all of its impulse at one time, so you'd need to accelerate the vehicle with a lot of Gs to do a successful pad abort. Rockets are a better solution simply because they can impart their impulse over several seconds, reducing the necessary G load down to the 8-10 range. It's like the old days of ejection seat design. The first ejection seats used compressed air or a cannon shot (really) to get the pilot clear of the plane's tail. As planes started going faster (and tails like the one on the F-104 were developed*), the old ejection seat design just didn't cut it anymore. In addition, they didn't work when the plane was low and/or slow, which means that if you had a real problem on takeoff or landing, you were screwed. A cannon shell powerful enough for a zero-zero (0 airspeed and altitude) ejection would've pulverized the pilot's spine, so rocket powered ejection seats were developed.

I like Tom's idea of short duration high thrust rocket motors to use the onboard maneuvering propellant for an abort. It could work with minimal dead weight (the abort engines and some bigger propellant lines with associated valves) assuming there was enough propellant to fire the rockets long enough for a pad abort. Suppose the crew compartment and crew weighed 10,000 pounds (number from the anal data store). You'd probably need to accelerate at least by 8Gs for 4 seconds, so you're talking about 80,000 pounds of thrust. Hypergolic propellant like that used for thrusters has an Isp in the 310 second range, so you'd need about 258 pounds of propellant per second, or a little over 1,000 pounds of propellant in all. That's fully reasonable given the propellant carried for orbital insertion, maneuvering, and reentry. Depending on where the abort engines were mounted and the overall vehicle design (e.g. Soyuz-like capsule with multiple sections or a more reusable design), you might not have to waste the abort system with each flight like you do with escape towers.

* The first F-104s to enter service used downward firing ejection seats to avoid the tail. If the pilot had a problem at low altitude, he was supposed to roll inverted and eject. Yeah, right. Later F-104s were fitted with upward firing rocket ejection seats. Unfortunately, some of the pilots who had flown the earlier models still had it ingrained to roll inverted and fire at low altitudes. Made for a real mess. Bummer when that happens.