Since the skin depth of copper at 1Ghz is about 2.3 micrometers, it doesn't seem like aluminum would provide a worse signal to noise ratio.
7075 aluminum is also much more resilient and stronger than pure copper, so it should be able to bend more without breaking.
The main problems seem to be splicing wires (due to oxidation) and Power over Ethernet, but for other uses, aluminum wires seem like a cheaper and lighter (for aerospace) solution.
So why do we still use copper for data?
Aluminum oxide is stable, hard (as sapphire, because it IS sapphire, aka alumina, Al2O3), and nonconductive. Oxide grows spontaneously on contact with air, so an aluminum electrical connection is often unreliable. Welding works, and some (fluoride-based) fluxes can allow soldering, but for crimp connections, you need antioxidant pastes and/or odd mechanical contrivances. Reliable aluminum electrical connections are messy or bulky.
Copper is compatible with a variety of insulation-displacement connection schemes (basically, just a hard clip that dents the copper but cuts through plastic insulation), that stay reliable for years. The clip parts can be made of copper alloys, so there are no dissimilar metals issues. Copper oxide is neither hard, nor insulating (it's a semiconductor), so copper wire just makes a better connection.
To put a simple summary to the existing answers:
Aluminum isn't commonly used in wire because while it is a fair conductor, it makes a mechanically poor wire.
Rdtsc gave a very good link in a comment. That list is a run down of all the problems you will encounter when using aluminum wire.
The short of it is that aluminum has poor mechanical properties for use as wire.
A short list of its worst properties:
It also has poor chemical properties - the oxidation that Whit3rd mentions.
Oh, yeah. It is also not easy to solder.
Looking at a conductivity table 7075 aluminum alloys have worse conductivity than pure aluminum, nearly half for some of them. Also, Wikipedia says the 7075 alloys are rather expensive (relative to other aluminum alloys), but I don't know how they compare to copper price-wise. These issues together probably explain why despite the 7075 alloys being available for over 70 years now they don't seem to have been used in any electrical applications. As @Harper correctly mentions below, the 8000-series aluminum alloys are the ones usually used in electrical applications.
The current way to make cheap data cables is copper-clad aluminum (CCA). You can help yourself to the ASTM B566 standard and see what's the exact composition of the ideal CCA cable (which doesn't mean that your Won Hung Lo manufacturers will even stick to that.) It's about 10-15% copper and the rest aluminum. For a summary of CCA cable properties from a manufacturer thereof (adhering to the aforementioned standard) see this page, for instance. There's also an ISO 13832 covering CCA, which seems to just incorporate the aforementioned B566 standard when it comes to CCA. UL also references that B566 in their testing services.
Do note however that no CCA cable can be currently and legitimately be advertised as Cat 5e/6. That's because those standards mandate copper; more details over here. Although I know of a ISPs with millions of users using CCA [for final customer-premises connection] and it seemingly pays off for them... even at 1Gbps speeds. But they can afford to test cables to their own standards in-house. Also note that CCA cables also don't conform to some [US mainly] building code standards; the ISPs I made reference to are located somewhere in Eastern Europe (although in the EU); they are also using mostly Huawei equipment.
In contrast, the ANSI/SCTE 100 (2010) standard for 75-ohm coax however allows for B566 CCA cable core (the 10%-copper grade); and it's good for 5MHz-1GHz operation (with -20dB SRL).
I don't know (or care) much about USB cable standards to tell you exactly what they allow or require...
Cheap 75 ohm coax as used for TV typically has loose aluminum wire braid shield with thin thin aluminum wrap. I think the centre conductor is copper-plated steel.
Nasty cheap stuff, but usable when crimped.
For very fine 24-gauge ethernet wire, there's just not enough metal there to make much of a difference in total cost of cable fabrication.
