Resistance heating is so 20th century. Granted, you likely cannot do a DIY air source heat pump build, but the COP is so high for such systems, that it's probably worth it to just buy it.

My mom had a Heat Pump water heater at her house and I was always having to go and fix it or clean the filter. It would start beeping loudly in the middle of the night when it wanted attention. The hot water was frequently not very hot.

Hopefully the new heat pump water heaters are better. The advantage of resistance heating is simplicity and cost, with no moving parts. Solar panels are so cheap now they make it hard to justify the expense of the heat pump, assuming you have room to mount the panels.

a COP of 4 can certainly justify having to install 3-4x less panels.

it disappoints me (but thrills me) that improvements in PV efficiency and cost have made solar thermal hot water more or less pointless.

Heat pumps have COP of 4 when reaching temperatures needed for room heating. Hot water is way hotter than that. The more the difference between outside air and heated water, the less the COP becomes. I don't expect COP of 4 at 200 fahrenheit

True, but you never need 200F for DHW. This is even dangerous (scalding) and harmful to the piping. Typical temperatures for heat pump derived DHW are around 120F (45-50C), with some (bi)weekly cycles to avoid legionella build up at 150F(65C). Your statement is generally true, because a heating installation that is optimized for heat pump works at 85-100F, however in practice not many installations in old buildings are like that.

If your concern is storage you want as hot as possible, less boiling. Thermostatic mixing valves can bring the temp down to a safe temperature for use.

Losses are higher but you store more energy per L, which is often the limiting factor.

Is energy per liter often the limiting factor? Suppose a 70m² apartment with 3-meter ceilings costs US$3000 a month because it's in an expensive city center like San Francisco or Manhattan. That's still only 17¢/liter/year. Expanding your hot water storage space from 45 liters to 200 liters consumes space worth US$27 per year of your rent. Even that cost seems far too low to be a limiting factor, and the vast majority of people live somewhere much cheaper than that.

I think that what actually costs money is not the space but the tank. Higher temperatures mean not only more expensive materials and shorter lifetimes for tanks and piping but also higher conductive losses.

As hot as possible is not the way to go. Heat pump COP will degrade dramatically if you try to boil the water. It is not even possible with the popular refrigerants (R32, R410a and even R143a), because they will exceed their critical temperature. If you cannot afford the space for a bigger DHW tank, then there are two options:

1. Consider PCM heat storage (still relatively new technology, but works well with heat pumps)

2. Maybe the problem shall be solved at the building level, not individual apartments.

But you only need to store enough for a day or two. So you can alternatively just go bigger