I agree with Robert,
The engine starting battery is isolated to be sure it is available to start engine after house banks have been depleted. Also the engine starting battery isn't a deep cycle battery but a starting battery, so it is designed to deliver high amperage for a short period. Although that sounds good for a windlass application the starting battery doesn't drawn down starting the engine like it would lifting 150' or more of rode.
A frustrated captain trying to "break free" a stuck anchor would certainly damage a starting battery before it was evident.
Some boats have a dedicated windlass battery right next to the windlass. This is good for several reasons. Cables to windlass motor which are big and expensive when done right are shorter. Cables to charging from shore power battery charger and alternator regulator are smaller, lighter and far cheaper. You would need a sizable deep-cycle battery for this job but it might be the most elegant solution. Of course even more weight in the ends of the boat cause hobby horsing too...
I think (and there are as many opinions on marine applications) your best bet is the house bank for the windlass and use the engine's alternator to buffer the load from the windlass. Most folks will be at idle speed when anchoring so the engine's alternator's output would be about 25 amps at most. That is not enough to protect a starting battery. A big house bank will shake off this load.