That's one of the trio of real Trek combat oddities:
1) Why fight at impulse when warp is an option?
2) Why fight at point blank ranges when weapons demonstrably reach farther?
3) Why raise shields only at the very last moment?
These might be related issues, tied to power allocation. Perhaps ships at warp cannot shield themselves because the engines consume too much of the available power, or because shields during warp have to be configured in a special way. Shields might consume a lot of power, yet beam weapons might only pierce fully powered shields when fired right next to them. None of that is completely satisfactory, though.
It could also be argued that warp fields are easily collapsed by enemy fire (we see this happen in "A Time to Stand", say), so there is no particular advantage in waiting for the chasing enemy to do the collapsing.
The thing is, Star Trek combat is not just a rehash of any specific style of nautical warfare from Earth history. It is a mixture of several elements, with idiosyncrasies of its own - which makes it a bit more plausible than "battleships of Jutland in space" or "carriers of Coral Sea in space" or "frigates of Horatio Hornblower in space" or whatever. Plausible in the sense of there being more unexplained lacunae there, that is: we can insert explanations into those even when the writers and effects people don't do it for us.