Your post is, "That year is also prone to random, not easily diagnosed, overheating events which make it prone to multiple or excessive overheating, which is bad."
This statement is FALSE.
Maybe I should explain this further.
The 10s up don't have a temperature gauge, but instead use a warning light that is blue on initial cold start and goes out as the engine temp comes up. If the engine runs hot, the light comes on red, but by then it's too late.
It's been my experience with these engines, the EJ253 of all generations, is not prone to overheating unless a failure with a hose or cap allows for coolant loss, a thermostat starts working, or rather not working, sporadically, or a cooling fan stops functioning.
Sometimes a single overheating event causes a head gasket breech, sometimes it takes more. The head gasket design is poor, we all know that, but the failure with the head gasket is the oil leaks caused by the corrosive nature of the oil eating away at the bonding material, not the coolant. The oil ports are on the outer parameter of the head while the coolant ports are in close to the cylinder, so the oil issue does not directly affect coolant seepage in to a cylinder. But if you look at the bonding material of the gasket, it is incapable of keeping a seal when the temperatures get too high and the expansion of the metals allows for easier breech events. The engine and gasket material is designed to withstand temperatures to a certain point and it is assumed by the engineers that the owner will be attentive to the car and what's going on. By this I mean regularly checking the simple things like oil and coolant level and being observant for any signs of a leak.
And in case anyone reading this does not know it, oil helps control engine temperature and if the level is low due to a breech in the HG or otherwise you lose lubrication and get an increase in friction - which creates heat - and the oiling system's ability to transfer the heat. Low oil levels increase combustion temperatures due to high cylinder wall temperatures and piston heating. This can create an environment for knocking/detonation and higher fuel consumption. Low oil also creates high temps on the bearings and all moving parts. This heat transfers to the surrounding metals in the engine and the coolant system has to keep up with it.
This is why when you replace the head gaskets on an EJ you go back in with the MLS gasket and not the OEM. It gives you a broad range of protection in not only containing the oil but also with the expansion of metals at high temperatures should the car overheat.
The engine is not prone to overheating unless there is a failure in temperature control due to leak, thermostat or cooling fan operation; many times these things in conjunction with low oil level are the cause for HG failure that allows for a coolant leak in to a cylinder.
As for overheating after an HG repair, if the person who performed the repair did not do a thorough job, then yes, a repeat will occur somewhere down the road. You can't use a Google search as justification for an incorrect statement and belief. You could find all kinds of misinformation on a Google search and it still comes down to the ability of the person attempting to diagnose the issue, whatever that issue may be.
I have a 2010. I bought the car knowing it needed repairs. The owner advertised it as having a leaking heater core which is a 4 hour repair plus the cost of the core. It also had other issues that were apparent at the time. The heater core is not leaking. I replaced the hoses his "mechanic" removed and there's no leak. I also did some checking around and found that the thermostat was also removed, apparently to keep the cooling system from building pressure. The head gasket was leaking in to cylinder 1. The "mechanic" could not isolate a head gasket issue because he did not know what to look for in locating the exact cause for the coolant loss and overheating. That is a failure on the mechanic, not the engine. What caused the breech in the first place? Could be anything like I've mentioned above. The HGs were leaking oil, there are fairly new coolant hoses and clamps on the system.
It's not the engine. It's the guesswork that goes along with inexperience or ignorance - sometimes laziness - in diagnosis. Nothing is hard unless you make it hard.