There were very few TNG warp chases where our heroes would have been the hunter and the enemy the prey. In fact, the only example that really comes to mind is "The Survivors", where Picard chases the Husnock with apparent destructive intent - but never closes the range for firing. In other chases, such as after the Borg Cube in "BoBW II", our heroes have not tried to destroy the fleeing enemy with weapons fire, for various reasons.
OTOH, the reverse was true a couple of times. The Borg chased the E-D at high warp in "Q Who?", and fired those strange green bolts that drained the hero ship's shields. And the Klingons fired at the E-D in "Emissary" while rapidly approaching our heroes; since they essentially opened fire just after entering visual range, one would expect them to have been approaching at warp. This is not explicit in the episode, however.
Certainly our heroes didn't express surprise when weapons fire (including energy beams or energy bolts) reached them in a warp chase. This opposed to e.g. them repeatedly musing that a phenomenon they thought warp-incapable was moving at warp.
I'm specifically getting at whether the dearth of warp speed combat (with phasers) in TNG was due to the adherence to their published TNG:TM...
Now that is an interesting question. But if there was "adherence" there, it was half-hearted at best, because aliens were allowed to fire warp-speed beams with dramatic impunity.
I might suggest the dearth of warp fights was due to the cost of the warp streak VFX: they could use a certain set of stock warp scenes to portray generic warp travel, but a combat scene would have required special VFX (such as in "Q Who?") where every added element, such as phaser beams, would hike up the cost.