That depends on your generation capacity and what the rules of your grid are.

If you're capable of producing enough power to run your home most of the time, then being grid connected and buying peak load from the grid itself rather than browning out your own devices might be a worth while tradeoff.

Most of us with grid tied solar installations (like me) transparently buy and sell electricity to and from the grid depending on day conditions. I buy from the grid overnight, and sell excess capacity during the day. Depending on how much electricity you use a battery system will smooth those out, but you need a lot of batteries to eliminate the need completely (OP mentioned 48KWh, which is about 3.5 Power Walls).

In my area the grid is really reliable and fees are low, so buying batteries is not economically viable. I'm currently paying $5.24 per month for a grid tie, which is below my threshold for caring.

It's also more viable to be grid tied if your winter needs are more than X times your summer needs. My 6.6kW array generates roughly 3x what we need during summer. But our home is heated in winter (at 6000' in New Mexico) using electrically powered air-source heat pumps (aka "minisplits") and that takes about 3x what we generate during the winter.

Adding either on-site storage capacity or sufficient additional panels to cover our winter needs really makes no sense. The storage capacity would have to be immense, because no matter how you slice it and dice it, we do not generate enough power to heat our home for several months (and that's with adobe and some passive design). The additional panels would take up a large amount of ground space, and result in us generating 9x our needs in summer.

I prefer to put my faith in the emergence of grid-scale storage solutions than try to solve this on a just-my-home level.

If the grid wasn’t reliable, a hypothetical I know, it would probably be cheaper to switch over to a ground source heat pump rather than increase your panels by 3x. That would lower your winter electricity demand, albeit at the cost of significant capital expenditure.

Does a ground source HP use that much less electricity than an air source HP?

Yes, by far. It’s much easier to extract heat from ~55F ground water than from ~20F exterior air. Ditto for dumping excess heat into ~55F ground water than 90F exterior air. On average the water coming out of a geothermal loop will be more advantageous to work with than exterior air, which is why it’s a thing.

The vehicle I'm currently sat in at the moment has a 32A electrical cable running in the back, currently pulling 2881W into a magic box provided by victron inverter/charger, that is used to charge a battery (which is currently fully charged). That battery is currently being drained at a rate of 2881W to run the equipment (via the inverter back to 230V)

If I pull the 32A cable, everything carries on working (I believe it's a sub-20ms switchover). If the power goes for some other reason it carries on working. The truck can run on a 230V/13A source just as well (although when the aircon is on - not needed currently - we'll be pulling more than 13A so the battery will slowly drain). I can even plug into two different inputs.

Now this is a mobile vehicle, and I'm no electrician, but my understanding is this is perfectly fine -- the victron presumably switches from the grid if the input is lost and doesn't feed anything back into the grid.

Presumably the same setup could be used to power a home instead of several racks of equipment in the back of a truck.

That Victron box has an automatic transfer switch in it, and is certified for permanent grid connection.

I'm getting a manual transfer switch installed - I live in the city (although it's rural-ish where I live) but we get occasional power outages and it's often enough (and long enough) to be worth the annoyance of getting a generator and switch installed, but not enough for me to shell out big $$$ for a natural gas generator and automatic transfer switch to ensure 100% uptime for my house.

This works well as long as there is a reasonably high chance of someone being in the building when the power fails. For many rural setups (for instance: weekend cottages) that isn't the case so more and more inverters come with an automatic transfer switch built in or for a small surcharge as an option.

Or if you travel. If I ever get a generator installed (with automatic transfer switch), it would be primarily for the case of a power outage during the winter when I'm not around.

I'm not sure about Ontario, but in many places you can be grid tied which means that you use both. While it is possible to change depending on conditions, the equipment to do that isn't very common. Solar systems are just starting to come out with single outlets that can run while the sun shines without the grid, but that is rare, most assume 100% on grid, or 100% off grid.

You can have a backup generator (with a transfer switch)--which many do in more rural areas at least in the US.

In some areas, there is both, but it requires having a correctly installed automatic disconnect, that cuts you off from the grid if the grid loses power.

Many/Most home solar installations do not correctly install one, which can be dangerous to linemen.