Most of what I am saying has to do with the US, I have no idea what happens in other countries. From what I can tell, this is the background information that is true about aluminum use in the US.

- In the 1960s they started using 1350 alloy aluminum wire, had problems with creep/cold flow, oxidation, strength, and thermal expansion
- 1350 would oxidize to make high resistance connections, thermally expand and creep to make low surface area connections, and was a weak material to work with
- Revised CO/ALR devices with indium plated terminals can usually be used with 1350 because the indium metal seals tightly to prevent corrosion, but doesn't solve the other problems (expansion, creep, strength).
- After that fiasco, 8000-series aluminum alloys were used for aluminum wire. Stronger, less creep, less oxidation. With anti-oxidant compounds this works A-OK, problem pretty much solved.
- Aluminum terminal blocks and bus bars use 6101 or 6061 (most of the time, for the ones that weren't recalled), more structurally optimized, not as oxidation resistant but often tin plated.

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So we solved aluminum wire, but it never really returned to low-amerage branch circuit wiring in houses. Smallest aluminum you typically see is 4AWG for 50A circuits, but even there 6AWG copper is still used a lot. These installations of aluminum cable must use an anti-oxidant compound on all terminations, and they all much be rated for use with aluminum.

Now if you are gonna have to do that for every termination, using aluminum for branch circuit wiring would suck. But that isn't always true, as copper clad aluminum wire exists. You can get CCA wire in sizes as small as 12AWG for 15A circuits, and of course it is cheaper and lighter than the 14AWG copper counterpart.

This wire uses 8000-series aluminum alloy, and is coated in copper to prevent oxidation. No anti-oxidant needed. Almost all terminations rated for Cu are rated for Cu-clad Al. But the thermal expansion issue still persists, and some say the cold flow issue was not entirely eliminated with 8000-series alloys.

What do you think? Will aluminum catch on for residential again? Or is this another disaster?

If a house costs like €300.000 to 800.000 to build and buy the land for, i'm not gonna care about €500 in extra cost of cable. I'd rather have copper in my walls and just be able to terminate anything to everything using bog standard connectors.

Copper wire is expensive but not that expensive. I pay €1 per meter (give or take a few cents - less for larger rolls) for single core 2,5mm² copper residential installation wire, rated for 16a 230v in the Netherlands and 20a 230v in Belgium. You write that stuff off in maybe 50 years or so if you install it right. The yearly cost is small compared to all the other things you gotta manage on a house.

It is true, the aluminum is more than double the conductivity of copper per conductor weight (not cross section, really weight), also way cheaper, but these aspects are not that significant on thinner wires. There the surrounding accessory (the insulation, restriction to the cable assembly materials to prevent corrosion, more care so more expense needed for termination,...) either cost the same or even is more expensive with aluminum, so if the material/weight savings are not substantial, it does not make much sense.

Regardless of the exact composition, aluminum are all more prone to oxidation and creep problems. The improved composition made them less severe, but compare to copper, they are still there. And some of the ways how to address these problems means more expensive terminal designs.
Now these problems affect mainly thinner conductors, the thicker the thing is, more resistant it becomes. So for relatively thin home installations they are way too much problem vs how much cost and weight savings it may offer vs copper, or the fixes for the aluminum problem become relatively expensive (big part of the extra termination cost to fix the aluminum problems does not depend on the size/rating of the connection, so for low current ones becomes pretty expensive). But for higher current, thicker conductors have inherently less problems to start with, plus the amount of material in question becomes so much it starts to make sense to invest into the more complex connection solutions.

And this is reflected in the standards - aluminum is allowed only 16mm^2 and above (AWG6 and thicker)

For normal home 16A circuit installation the 2.5mm^2 of copper is used (4mm^2 was used with Al),
that in the equivalent 4mm^2 Al, was and in older installations still is causing permanent headaches with connection resistance faults.

Only the main feed and distribution lines, generally significantly thicker than the 16mm^2, are still installed and used with aluminum without any problems. But the important differentiator is the conductor size.

The problem with aluminum wiring was never 'solved' as it is physically/chemically fundamental. For smaller gauges there is also a significant corrosion problem. Of course, financial savings are large, and sometimes lower density of aluminum matters, so Al wiring is tolerated in professional installations. And thieves are not interested in stealing Al cables. Home wiring is more chaotic and less controlled by definition, and especially in US with 120V line voltage is unavoidably associated with huge currents. So, please NO )

Most remodelers I have seen at HGTV tells the viewer that the house with aluminium wiring should be replaced with copper wiring to bring it's up to code.

Well, if it is up to code valid at build time, it is "up to code" now as well.
Problem is, when the installation is too old, you will have troubles finding components compliant with code from that time. Especially things compatible with aluminum wires (switches, sockets, connection for pigtails,...).