Your alternator, when engine is running, has much more capacity than the 200 watts of solar
Yes, your alternator can theoretically deliver much more current than your solar, but it won't. The difficulty is that, as RD has often lamented, the internal resistance of your house battery coupled with "Ohm's Law". This 'one-two' punch results in a much less than expected initial charging current (from your alternator to the battery) that drops surprisingly quickly to only a fraction of this initial charging current.
So what good is a high capacity alternator if you can’t use it? Well you can - - just not charging your house batteries. Drop a ‘big ole load’ across your battery (such as our induction cooktop running a sine-wave inverter with its 150 ampere demand) and see what happens. Your alternator will come to the rescue and will supply all (or most) of the required energy.
What we really desire is a multi-stage charger that has a true constant current “bulk” charging capability . . . in our present discussion, one that supplies the maximum 0.15xAH capacity, or 24 amperes. There may be such chargers out there, but all the sophisticated multistage chargers we’ve played with fail to perform any better than simply placing your house battery across your alternator.
Ahh but solar is different. Solar, depending on how many panels you have and whether they’re wired in series or parallel, operates at a much higher voltage - - ours . . . in the order of 30 VDC. This gives the solar controller a huge advantage over your 14.4 volt alternator . . . this allows the solar controller to output its full current (or whatever lower current you may have programmed it to output) continuously until a given charge condition (like 100% charge) is reached. You can set your controller to output the maximum safe current for your battery, again in the example being discussed, 24 amperes, until the battery is fully charged.
Don’t sell your solar short. We, in fact, normally disconnect our alternator and let the solar do its thing.
But to better understand what’s going on, we like the idea of the clip-on ammeter . . . and suggest that you include a shunt/ammeter in your system so that you can see - - at any given instant - - precisely how much current your batteries are supplying or are being recharged.