I think I can contribute something to this thread, or at least try.
There are at least four ways to join the house battery (or bank) to the start battery (or bank). Let's look at each of them.
1) Direct connect cabling.
2) Automatic Charging Relay (e.g. Blue Sea ACR)
3) Remote Battery Switch (e.g. Blue Sea ML-RBS)
4) DC-DC Charger (e.g. Victron Orion)
5) I guess I'll add: Classic 4-way A-B-Both-Off switch
How do these differ?
1) Direct connect cabling essentially joins the two banks into one new bank. This is least desirable for a bunch of reasons I won't bother elaborating upon.
(Both banks should be the same chemistry, age, and there are other best practices when building a bank that I won't get into.)
2) ACR is a nice way to ensure whenever one battery or bank is getting charged that both are getting charged (whether they need it or not). It is automatic. If one bank is attached to an alternator, and the other is attached to solar or a shore power charger, or anything, either bank's charging activity will turn the ACR on, and both banks get charged, whether it is desired or not. When there is no charging in-place, the relay opens, and the drain on one bank only affects that one bank. If both are in discharge state, they discharge separately. The Blue Sea ACR enables a remote light indicator so the captain can see when it is open or closed from the helm, which is nice. Both banks should be the same chemistry.
3) RBS is a nice way to temporarily join to batteries or banks together in case you want to temporarily charge one from the other, or join them together in order to get a boat started if the start battery is low. The big feature of the RBS is the "demand" to join them temporarily is bi-directional. Either bank can "help" the other. There is no "intelligence" or automation built into this system except that of the captain who chooses when to turn it on, for how long, and remembering to turn it off! LOL The chemistries should be the same. ((Side note: Most Lithium batteries do not "like" to be used for starting loads, and it'll void warranties etc.))
4) The DC-DC charger is a uni-directional way to ensure one "output bank" is charged from the other "input bank"... with intelligence such that if the output bank is really not in need of a charge (e.g. 100% SOC state of charge), there is no flow until that changes. This is really the only advisable way to join two banks together that are of different chemistries or different age ... or different in other ways, (e.g. Lithium with flooded lead acid), in which case, you program the DC-DC Charger to let it know which chemistry the output bank is, as they have different charge profiles.
The only disadvantage of a DC-DC Charger is it unidirectional, and perhaps cost. If you need the "output bank" to be joined to the "input bank" for some reason, it simply does not provide for that, which is not a bad thing sometimes!
DC-DC chargers typically have a remote switch to manually turn them on and off, OR only have them "on" when the engine is running.
5) The classic 4-way switch is the simplest way to do this. But, you should not make changes to this switch's position when the engine is running. It *may* toast the diodes in your alternator, disabling it entirely. To make a change it is best to turn off the engine, make the change, then restart the engine. Like 2 and 3, the chemistries should be the same.
To the original question of this post, my short answer would unequivocally be "Yes, I would want to be able to charge the house bank from the alternator when underway." But with the following caveats: a) "... IF there is no other way to charge those house batteries... e.g. no Solar no second alternator, etc." b) I'd prefer to be able to turn the charging on and off. c) They have to be the same chemistry if being conjoined together.
My best choice of method (2, 3, 4, 5) would depend upon other things, like budget, size and age of each bank, etc.
I've used each of these methods on different size boats and configurations over the years, and they each have their place! Hope this helps.
(Other considerations to get right, which I won't get into: Cable size, Circuit Breakers, how and where to mount the "stuff".)
