I did the house power charging with only an ACR for a year and a half. It worked merely okay. The issue is that I rarely drive long enough to get a nice full charge on the house battery ever, plus being a 105ah AGM I'd suck it pretty low on a dark winter day with lighting, electric blanket at night, USB/12V accessories. Needless to say the alternator would rarely get the house battery to take a full charge. You could literally drive all day, then upon getting home plug in a battery charger at 2amp trickle and it would still charge for another 5+ hours.
Orton is right about battery health and charge: Deep Cycle AGM have different charging requirements than a lead acid automotive battery. They like staying topped up, they like a multi-stage charge, etc. Short bursts of 20+ amps off the alternator at 14.2V just doesn't cut it. It works, but not optimally and in effect leaves you with a battery that is always 20-30% down on charge.
Over a year and a half the battery began to show signs of sulfating. You could charge it up with a trickle charger and it would say 100% and 12.7V, but as soon as you put any load on it it would quickly fall to 12.5 or less. My battery shop has a de-sulfating process that they ran on my AGM and bam, it's good as new now. Holds 12.8V and has serious CCA—more than original surprisingly. I then added 200W of flexible solar taped to the roof. Now I'm laughing. Solar may be the single best electrical upgrade I've done. With moderate sun I can power my Engel 47L fridge, MaxxFan, and USB charging all day with no cumulative draw on the battery, plus the multistage charger gives the battery a nice solid charge. With my 105ah AGM, 200W of solar, and fridge/fan/webasto heater/USB/lights, I am fully charged everyday by around 10 or 11am (in the summer). When the sun goes down my battery goes from 12.85V down to about 12.45ish overnight (the lowest I've seen thus far is 12.3 in the morning when I didn't get good sun the day before). This is night and day vs. my ACR only setup which would regularly see 12.7 fall to 11.9ish overnight with the same or less loads.
Solar for the win. Even a cheap setup like my Amazon special homebuilt setup makes a huge difference. House battery fully charges on it's own everyday without thinking about it. The multi-stage solar charge controller gives a much better charge than just applying alternator amperage to it. Running the fridge 24/7 is now a viable option for multi-day camping trips. It's cheap. My 200W system was $600 all in. If I had gone for hard panels vs the flexible ones it would have been more like $450-500.