Hooey that contradicts basic electrical concepts.
Computers designed by engineers provide sufficient power: sufficient current on each voltage. That original supply was more than sufficient. How is a supply 'integrated'? It's not. Numbers originally posted by fgbowen define what really matters.
Not within the real world context of what wattage and currents are available in existing PSU, vs what the specific system in question needs. The original supply is rated in particular situations including ambient temperature, and that only for the period of the warranty. MTBF figures fly out the window when applied to actual component lifespan.
The numbers mean very, very little. The numbers that actually matter are what the system actually uses, and what specific discrete component(s) in the power supply failed, since we can be fairly confident it was not the currents or it would not have lasted until now. In the end, neither we or the OP can pick a number for every power rail, we're not designing the PSU from scratch but instead the choices are among what is available in the market, whether any (or all) available PSU meet the numbers the system needs, not necessarily are equal to those of the prior PSU.
A ripple claim had no numbers. Common when information is only from subjective reasoning. Knowledge means 'too much ripple' was defined with a number. Many techs have no idea how to even measure ripple voltage let alone know what it is. Also irrelevant to the OP's questions.
Quite relevant if excessive ripple caused accelerated aging of capacitors in the PSU. Perhaps you do not frequently encounter PSU that fail for this reason? It is the number one failure mode of budgetized power supplies within a period after early infant mortality yet before the fan was expected to fail from # of power-on hours.
What really happens during an excessive load? Other factors take charge including foldback current limiting. Why was current limiting ignored? Many techs have no idea what foldback current limiting is. Nor why excessive loading does not create excessive ripple voltage. First one must know how much ripple is excessive.
In the real world, a power supply rated for (n) amount of current, cannot necessarily sustain this continually even if it is a more conservative figure than only peak rating. At this point one must look at what portion of the supply degrades at any particular current level. In the end, all we really need to see is why the original PSU failed and take measures to not have that happen again, unless it is acceptable that the tour of duty for the replacement be the same as for the original. Some may consider that acceptable but I do not as I don't consider a PSU to be a part that should be considered a wear item that needs replaced within the lifespan of a system.
Unfortunately some even heard that low voltage causes semiconductor damage. When even manufacturer numbers say otherwise.
I have already sufficiently explained why this is possible, that the lower the input voltage on a regulated output subcircuit, the higher the current necessarily has to be. Further, low voltage within the context of a switching power supply generally causes higher ripple voltage. Check power supply review testing if this is doubted. If we can conclude that indeed, higher loading to the point of voltage droop results in higher ripple, as testers do consistently measure with a scope, then we can move on to what higher ripple does.
With higher ripple, you must have a higher average voltage to retain stability because the equipment must not only be stable at the average voltage but also at the low value in the ripple waveform.
Computers designed by engineers have insufficient airflow? Nonsense. A properly designed machine must work OK even in a 100 degree F room. Airflow at 70 degrees is more than sufficient since airflow must be sufficient even at 100 degrees.
Computers are designed by engineers for climate controlled conditions unless explicitly stated otherwise. Instead, engineers are given directions to tailor the system towards lower noise, reduction in number of fans, and in the case of this system, the slim profile. Further, it is a well known fact that a rise in temperature causes a reduction in lifespan and this is what we may be seeing, a system where the PSU ran hotter than same components would in a better ventilated system, and eventually had an earlier failure as a result. Did it last for the warranty period? If so, beancounters have instructed the engineers on the low cost path to make that happen.
Of course, if airflow was insufficient, then the claim provided a number that defines 'insufficient airflow'. No number provided for one obvious reason. Speculation. Nobody said how many CFMs currently exist. How can anyone know that system has 'insufficient airflow' without knowing existing CFMs? Wild speculation. Systems designed by engineers have more than sufficient airflow.
You are suggesting engineers are magical creatures that can do no wrong, nor are subject to design limitations or authoritative directions? Quite the opposite, above all else it's about cost. Engineers would love to use a more robust transistor, higher quality fan, solid capacitors with nearly an order of magnitude longer rated lifespan in a heated environment like they see in a PSU.
If capacitors are undersized, then numbers were posted to define insufficient and sufficient capacitance. Nobody provided a number for existing capacitors. How does he know that capacitance is insufficient? Speculation combined with subjective reasoning somehow becomes knowledge.
We as a community have a marvelous thing today in the internet. There are people out there that tear apart PSU and fix them, and years of data accumulated about capacitor problems resulting from not just faulty electrolyte but poor quality components that can't be extrapolated to meet the same lifespan ratings as quality components. For example you might have two capacitors, both seemingly rated the same at 3,000 hours lifespan at 105C temp, all other specs the same. They might both achieve this, but what if the consumer considers 3,000 hours an unacceptably short lifespan since that is only 125 days of continuous operation? That's where experience comes into play, which sources and formulations of caps are longer lived in the real world conditions of being in a hot running power supply.
And that is the point. Separate wild speculation from engineering facts. Wild speculation just knows something subjectively - no numbers. As if a feeling becomes truth. Knowledge is provided with the numbers.
Speculation is often the shortest course to the goal. Engineering facts would include accumulation of data that seems beyond the abilities of the OP, requiring both equipment and time worth more than the replacement cost of a ~ $40 PSU considering it still has to be repaired or replaced.
What is a quality supply?
In this case, it's any wattage that is available on the market for that particular form factor which is TFX (or whichever form factor) 12V compliant, as all models made are enough for that system config., and one built to have good lifespan. If there were significant system upgrades made then it would be a different matter, but a USB external HDD is not one.
Since I am goal oriented and have already picked my choice of what the best commonly available replacement PSU is, since this type of information bears on the resolution of the problem, I feel there is nothing constructive to come from further debate as we obviously don't have the same agenda.