Alloying is a red herring when it comes to welding, though, right? We don't need to alloy steels to weld them. We can weld elemental iron. The difficulty in welding aluminum is the electrically insulating oxide layer that forms on aluminum AND the very high thermal conductivity that gives a smaller margin of error before the entire piece melts into a puddle. So wait, yeah, alloying it to make the weld take without melting the rest of the piece would be good, but the difference is that aluminum is so much higher in thermal conductivity.
Yeah, conductivity is the big deal. If it had a substantial mushy range, like off-alloy solders (think of what 50/50 or 40/60 feels like, compared to near-eutectic 60/40), you'd be able to deal with that -- the metal matrix doesn't instantly melt when it crosses solidus, it can hold some shape before turning into a useless slump. But that range is so narrow, and the conductivity high, that you don't have much choice, and that goes for almost all alloys of aluminum.
Contrast with copper alloys, where elemental copper is even worse to weld (or so I understand), but the lower conductivity and much wider mushy range of many bronzes makes them quite easy to weld.
Same reason welding stainless is easier process to control (laying down a weld, anyhow; keeping it stainless is a different matter) than carbon steel, due to lower thermal conductivity.
Yup, both the mushy (liquidus-solidus) range and the conductivity work against you. Seems to suggests a kind of ratio between a bulk thermal time constant* and the desirable power density. Doing some materials with torch is easy, doing some even with arc welding is hard!
*Which depends on geometry: cross section, also ambient heat flow to a lesser extent.
Is laser or e-beam welding of copper a thing? I'd guess with the power density being another step higher again, it'd be pretty reasonable... Could also just be that, if you're breaking out such sophistication for a job, you're probably not going to mind putting in the extra thought to optimize fitment, preparation and process...
Wonder if... physics apparatus needs that much? Wouldn't think there are all that many industrially important assemblies, in copper, that couldn't be 1. direct cast, 2. machined, 3. furnace brazed (or other brazing processes), or other options, with laser and e-beam welding being fairly distant except for something that absolutely needs the e.g. chemical purity of a welded joint...
But I digress

Tim