In my country (Poland, so not much renewable energy unfortunately) night-time (and weekend) rates are significantly lower (in some cases over 50% lower). You may choose uniform rate but it's not worth it (just remember to do your washing at night).

I worked in a company that sold energy-trading systems for many countries in Europe, and it was similar there (usually individual customers may choose uniform average rate, or much better offpeak rate and slightly worse peak rate, while the big energy market participants trade with different peak and off-peak rates almost always).

Is this a real issue? My understanding was that there is a significantly lower demand for electricity at night. This is reflected in my energy tariff at least (daytime ~3x cost per kWh over night time).

Traditionally, the oversupply due to keeping coal and nuclear running at their optimum is available at night, when the demand is lower.

Many locations, like yours, already account for this by charging lower prices at night to incentivize people to shift their load to these times e.g. putting the dishwasher on a timer so it runs overnight. Many pumped hydro stations store energy at this time too, often they were built specifically to pair with nuclear stations to better map a steady supply to a variable demand.

In areas that are ideal for solar, and roll out solar heavily, they may end up in the opposite situation, with the supply and demand mismatch reversed and so try to push usage to the middle of the day by dropping the prices then. Since most usage is during the day due to air-con load and the fact that people sleep at night, this may mean lower prices overall.

Once you add the internet into the equation, rather than the blunt instrument of a block of hours at a lower charge you can do things like have specific plugs for electric cars or an irrigation pump on a farm that can respond on a second by second basis to over or undersupply of electricity by using more or less in exchange for a cheaper rate. This is called "demand response" and while it happens already with big industrial users, it's getting cheaper and easier for it to be used by more and more users. One neat product that already exists is an internet connected car charger that checks the carbon content of the grid and charges your car overnight only when the wind energy is a big part of the mix.

Electric rates are the same around here 24/7. If it's more expensive to provide baseline load at night, increase the night rates.

Elastic uses of power, like charging car batteries, running the dryer, heating the water heater, etc., can be shifted to when power is cheaper.

I.e. reducing demand for night power is a cheap and effective means of dealing with the sun not shining at night.

Okay, so we ask people not to charge their EVs during the day and now we won't want them to charge them at night? I know EV penetration isn't high but many utilities have good rates at night!

The best way to fix demand is to get all usage to be as efficient as possible, not restrict its use