The Enterprise in TMP had yet to do any warp flow calibrations on the engines except on computer simulated runs. It had yet to run her engines at warp for real. Since the Enterprise had new engines maybe for the shakedown testing they do it away from population centers just in case something bad happens, and they don't warp into a planet, or a star, etc. After all when the Enterprise engines created the wormhole they lost helm control.
Captain's log, stardate 7412.6. one point eight hours from launch. In order to intercept the intruder at the earliest possible time, we must now risk engaging warp drive while still within the solar system.
DECKER: Captain, assuming we have full warp capability, accelerating to warp seven on leaving the solar system will bring us to IP with the intruder, twenty point one hours.
KIRK: Well, Bones, do the new medical facilities meet with your approval?
McCOY: They do not. It's like working in a damned computer center.
KIRK: Programming ready?
DECKER: Program set for standard warp entry, Captain, ...but I still recommend further simulation study.
KIRK: Mister Decker, every minute brings that object closer to Earth! Engineering! Stand by for warp drive.
SCOTT (on intercom): We need further warp simulation on the flow sensors.
KIRK: Engineer, we need warp speed now!
McCOY: Jim, you're pushing. Your people know their jobs
The result was the wormhole....
KIRK: Mister Decker... Wormhole! ...Get us back on impulse power! Full reverse!
SULU: Negative helm control, Captain! Going reverse on impulse power!
UHURA: Subspace frequencies are jammed, sir. Wormhole effect!
DECKER: Negative control from inertial lag will continue twenty-two point five seconds before forward velocity slows to sub-light speed.
ILIA: Unidentified small object has been pulled into the wormhole with us, Captain! Directly ahead!
KIRK: Forcefields up, full! Put object on viewer. ...Manual override on helm.
SULU: No manual response!
ILIA: Navigational deflectors coming up.
DECKER: Wormhole distortion has over-loaded main power systems!
ILIA: Navigational deflectors inoperative, Captain. Directional control also inoperative.
SCOTT: Captain, it was the engine imbalance that created the wormhole in the first place. ...It'll happen again if we don't correct it.
So that is the reason they were cautious the first time jumping to warp within the solar system, they weren't sure what was going to happen. They rushed the ship out before it was ready.
When Spock came aboard, he was able to help Scott get the warp engines balanced so they could go to warp at full speed...
Captain's log, stardate 7413.4. Thanks to Mister Spock's timely arrival, and assistance, we have the engines rebalanced into full warp capacity. Repair time less than three hours, ...which means we will now be able to intercept intruder while still more than a day from Earth.