First, hello.
Second, just wanted to add some info I couldn’t find (sorry if I missed it).
The hole thing isn’t exclusive to US plugs. EU standards from long time ago (German plugs) have round prongs, most of the same size, however, with little precision in manufacturing they ended up slightly a different size every time. In addition, “better” plugs were slightly larger, with high-powered devices even larger and thicker. As a result, the socket began feeling the strain when forcing larger prongs in.
Initially, there receiving end of the prong was a metal tube, about the size of the prong, and sliced longitudinally, much like power MOLEX plugs are now (The ones used in IDE devices for power). When inserted, the tube spread out a little to accommodate the prong. The insertion of larger prongs and the re-re-re-insertion of normal prongs meant that the tube got looser and in high use cases they let the plug fall out altogether or, worse, allow imperfect contact to be made.
As a result, sparks were common and the welding of prongs to the socket and electrical EM and shocks to the grid were rather common.
To allow for this fatigue, the prongs gained a slice/slit, longitudinally. This allowed the prong to shrink when jammed in a tighter spot, and, after being removed, one could use a simple screwdriver to spread them apart a little, in order for the socket to fit snugly and reliably.
As materials got better (copper got upgraded to aluminum and brass, and later better alloys) and designs improved (today’s plugs typically have two bend bands, spot-welded together, making them very resilient), the slot in the prong got left out, then the prongs got promoted to crimped tubes, which allows for less materials with plenty strength to spare. As much as 50% of the materials could be saved and the prongs are virtually unbendable by humans. It is not a widespread practice, though, especially in high power devices.
As the slot in the prongs were there to adjust for manufacturing errors and material wear and tear, I believe the same is true for the holes in the said bands. With electrical equipment being less than the dollar-worth they are today, people tended to keep sockets and extension cords forever, and a system was needed to make them work after twenty years of insertions with a good, continuous contact.
I don’t remember the original reference, but I do distinctly remember that the original design allowed for a “bump” in the target slot inside a socket to allow for the plug to be retained. As far as I know, the system was never implemented in any home equipment, but one can’t implement it if the holes aren’t there. So the holes are kept.
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There is no way a system can be improved, strength-wise, by drilling it. What the composite structure/honeycomb/drilled does is allow for a small sacrifice in strength for a bigger reduction in weight. When done correctly and with the right materials, the increase in cost is well worth it. Airborne engineering people are familiar with this, as a honeycomb aluminum structure can deliver most of the strength for a fraction of the weight, and, thus, the running cost.
The bottom line is, strength with a hole in it is less strength. A little less or a lot less, but less.
As for money, I do believe the cost of hole punching is well offset by the cost of saved materials.
The heat guy isn’t completely nuts, hot plugs are differently designed, but it will not make any visible difference.
Slots aren’t completely new as a concept. “Computer” sockets (C13/C14) use them, with no holes because the plug is snug from the rubber and plastic of the socket. Same heat, weight, strength issues - no holes. Same goes for a multitude of plugs in various countries that have no such holes, but what they do have is a system for plug retention.
And here are the standard Schuko plugs (non-adaptive). I can’t find any image of the slit prongs, probably because they died prior to the advent of digital imagery, but if I find one laying around I’ll take a shot and attach it. It’s hard to feel young after this 
Until then, I found this image. It is not a power socket, but it does illustrate the split prong I was on about.