Seems you're well situated without an inverter. Yet, an inverter allows flexibility for the unforeseen - - for example, we have this cute little Hamilton Beach coffee bean grinder . . . runs on 120vac. Then there's our portable TV antenna and preamp (we don't use it much either) . . . like most small electric appliances, it comes with a 120vac supply. While some of our small 'book readers' and tablets come with 'combo' 120vac/USB chargers, others only provide a 120vac power adapter. Having at least a small (sine wave) inverter would avoid the not infrequent hassle of having to acquire/provision a separate 12v power adapter.
But we come with a bias. Our DIY Promaster is an "all electric" design - - no LP gas. The center piece of our system is a Magnum 2812 charger/inverter that powers 9 duplex outlets throughout the (inside and outside) of the van. 'Electricwise', living in the van is little different than living at home.
2016 159" High Top DIY ProMaster with 500ah Starlight Solar/Elite LiFePo4, 810watt Kyocera Solar w/MidNite Solar Classic MPPT, Magnum 2812/MMP250-60S Charger/PSW w/remote, Nations 280amp 2nd Alternator with Balmar regulator, NovaCool R4500 12/120v frig, 2 burner TruInduction cookstop, SMEV 8005 sink, FloJet R4426143 pump. No A/C or indoor washroom.