There are possible parallels here to the shift from steam to diesel power in shipping, which began to occur around WW2 era (though most ships built for the war itself used steam plant). One notable example of a large, diesel-powered warship of that era was the Graf Spee.
A diesel engine can be started and/or throttled up in a matter of a few seconds; a minute at most for exceptionally large engines, or if actively trying to avoid thermal stresses to reduce maintenance needs.
A steam engine or turbine, however, requires that enough boilers have first been lit off and brought up to pressure to produce enough steam for the power ordered. Lighting off a boiler from cold can take literally hours. You preferably want to do that in advance of need, rather than having to delay any orders for high power manoeuvring. On the other hand, keeping more boilers alight than necessary is wasteful of fuel.
An entry in one WW2 submarine's log illustrates how this could be taken advantage of in combat:
A Japanese convoy was sighted, escorted by a destroyer. Japanese merchants were a primary target for USN submarines, to sever the logistical supply chain that kept every part of the Japanese military in operation. This convoy was sailing near the coast in shallow water, probably trying to make submarine attacks more difficult since a favourite escape tactic was to dive deeper than Japanese sonar could search.
The typical IJN destroyer had three boilers; with all three burning it could make well over 30kt in a calm sea, but to escort slow merchant ships it would light only one, limiting it to about 18kt. This would be fast enough to keep up with a Type VII or Type IX on the surface, but not a USN "fleet boat". Judging that was the case, the submarine closed in for the kill under cover of darkness. The destroyer would be a difficult target to hit, so the strike was aimed squarely at the convoy itself.
The first thing the Japanese knew about it was when a ship exploded. Thus alerted, searchlights were turned on and the submarine soon located. But it had already turned tail and run its engines up to - and beyond - maximum rated power, making for deep water at about 24kt. The destroyer followed, but soon found itself falling out of gun range, and as the sun rose, could only watch as the submarine disappeared over the horizon. The second and third boilers then came online, and the destroyer accelerated - only to see the submarine reach the edge of the continental shelf and submerge, out of reach.
So how does that translate into warp drives?
Well for a start, the fact is that stars, rocks and balls of gas are very predictable in their motions. Even a very cheap computer by today's standards could calculate the position and trajectory of every charted natural object in a ten-lightyear radius in a fraction of a second. I don't buy any argument that computing power is the limiting factor here.
So why the heck do you need to communicate with "several deep space networks"? Probably to file a flight plan to prove that your course doesn't intersect any other spacecraft's course. Spacecraft are objects that you can't reliably predict the positions of from charts loaded at the last docking. Space is pretty big, so the chances of a hastily chosen flight plan being accepted are high but the communication delays are potentially long.
Next, consider that 4c is very slow by the standards of interstellar travel. At that speed, starting from Earth, you have two whole minutes to figure out where the Sun is and change course to avoid running into it - and more than ten minutes to similarly avoid Jupiter. You don't need to start running calculations for anything in Alpha Centauri for the next year, even if you started out in that general direction. By then, one assumes you have run out of patience and figured out how to safely engage some higher speed.
But this low speed, and the presumably large size of a dreadnought-type starship, does make a couple of things plausible that would be difficult for a smaller ship to match:
If a warp drive takes time to physically spool up - even on the order of a few minutes - then a small one could be kept on hot-standby to eliminate most of that delay, and it would make sense for it to have less speed capability than the full-sized main drive. This would be less of a burden for a very large ship than a smaller one, due to the fuel reserves carried.
Also, due to a dreadnought's size and comparative rarity, it could keep a permanent reservation in the flight-planning system of several dozen relatively short and slow warp trajectories that radiate from its actual current position. At 12 light-days long, these would be enough to clear a stellar system in a relatively unpredictable direction, while waiting for the normal flight-planning negotiation to complete for a full-speed warp.