What happens at the connections ?
Indeed, that I suspect as the weakest point as well. I think it should be strictly screw type and inspected regularly.
And other suspicion comes from the sockets: Are the 120V sockets really permanent 20A rated?
Maybe it would really be a better idea to wire the ballasts as 240V, make a "Y" splitter box for the 240V connection (these are bigger and it should have less problems with the 20A) and then run the 240V into the lantyerns. Then according to the tables it will suffice even with AWG16 (as individual lanterns will be drawing just 10A; but I wouldn't make it less than 3x1.5mm^2, so AWG14), which will be cheaper and mainly lighter (and as well with lower relative voltage drop).
For example, what if the standard requires 2.5mm^2 +/- 10%, but the manufactrers make it 2.27 +/- 1% (just example) ? They would obviously get away with it according to standards, but would we get away with 25A on such cable ?
The standard already counts with tolerances and the maximum resistance as the consequence. The real problem is not that much the current density, but the power dissipation per unit length with the given temperature headroom. The power dissipation is then related to the outer surface of the complete cable, as that is, where the cable is cooled. That means maximum unity length resistance has to stay within limits allowed by the standard.
And there when I compared my calculation against the standardized resistances for the given cable gauge, the standardized resistance was about 30% larger. Part goes for the elevated temperature, part for not really 100% pure copper, but still there is about 10% extra margin, that clearly count for the allowed variation. So if the cable maker uses cleaner copper, he may use even thinner cross section and get away with it (actually this would be quite beneficial here, as it would mean lighter cable of the same capacity). Or if the maker wants to use lower purity grade copper, he has to use thicker real cross section to compensate for it and still it will be OK.
In any case all these calculations assume a good quality cable, fully conforming to the standard specification. If some product does not conform to it's specification, even factor of two overdesign with it does not guarantee it will work - because most likely the problem is not that much in too thin copper, but because the individual fibers are just broken. And that fault means such cable is in reality way weaker than would correspond to the resistance measurement (if a supposedly AWG10 has resistance corresponding more to AWG12, most likely majority of its fibers are broken and all the resistance is picked up on very short section, so it won't correspond to even AWG18 or so - after some corrosion, the high ohmic section will become way longer and so severely overheat the cable). Quite good test for this is how well the resistance matches among the individual conductors. If their resistance is closer to the maximum standard limit, but they differ less than 1% or so, it means the cable is designed that way and so it should be OK. But if two strands read 10% lower than the 3'rd one (assume they all are of the same gauge rating), I would throw such cable away, even when all would be 20% lower resistance than the standard requirements (because it means the cable itself was designed to be 30% lower resistance, but has a defect increasing the resistance of one of it's wires by 10%; that could well mean about 50% of the fibers broken around one place and short distance away the current gets redistributed again).
Finally, with some cables i seen on the market lately (all imported from the same overseas place) i'd suspect whether they are even compliant at all, but not allways there is choice what to buy
Before buying it, really inspect it, check the cut out and stay away from the cheapest sales (buy only at proven quality distributors)...
It is not only about how the cable was manufactured, but as well how it was treated during the distribution. It is not so "difficult" to waste even a peerfect quality cable by just careless handling (storing the drums outdoors,...).
