Hmmm! Thanks for bringing the "Mesmerizer" story to my attention, CaptainKal. I don't own that story so I can't bring his actions in it into context; exactly what it is it he does in the course of that story? What's the plot, more or less?
Superman uses a giant TV screen and simulcast on all TV stations to broadcast his own super-hypnotic commands to Metropolis for them to resist all other forms of hypnotism to make them immune to Spellbinder's hypnotism. He subsequently attempts to beat Spellbinder at his own game by super-hypnotically commanding him to surrender. This fails due to the special lenses 'Binder wears in his mask that weaken hypnotic effects.
Superman's codes are rather foggy when it comes to protecting his secret identity. For example, Superman doesn't tell lies, but he lies often to protect his secret identity. "I...suppose I just fainted when that Dinosaur came to life." And so on. It is interesting to note that Superman's use of Super-Hypnotism on Lois was related to protection of his secret identity. It may be interesting to hear how Superman would justify that sort of behavior, morally. Maybe Superman figures that it's "for their own good?" After all, knowing who Superman is potentially opens them for very dangerous reprisals, so it's not hard to follow his logic here. And all it takes is a brain-reading machine built by Luthor or Brainiac to obtain this information from their minds, even if they promise not to tell, so Super-Hypnotism mindwipes may be the best course of action.
This may account for why Superman hasn't used his Super-Hypnotism on Pete Ross, for example: Superman is unaware that Pete knows his secret identity.
Superman did become aware of Pete's knowledge when Pete's son Jon was kidnapped by an alien warfleet, so Pete didn't want to waste time with the fiction of pretending not to know who Clark really was. Pete even turned into a bitter enemy trying to kill Superman for not saving Jon. Yet, Superman never chose to mindwipe Pete in anyway, not via amnesium nor super-hypnosis, etc.
As for the Superspeed/Strength combinations that Superman now uses together: I get a sense they did the right thing for the wrong reason. "The right thing" is have Superman use his powers with a degree of intelligence - everybody wants a clever Superman. The wrong reason is that this sort of fighting style and strategy was made popular by the bane of my existence, the slow and loathesome and inexplicably popular foreign cartoon, Dragonball Z (who knew they had Image Comics in Asia?)
Fans have been speculating and demanding this portrayal for decades. DC just finally listened to us about the logic of it all.
It may be entirely possible that the writers were pointing out an error that simply isn't there. The laws of physics and common sense state that it just isn't possible to go from zero-to-20,000mph in a single step; Superman would require room to accelerate and build up speed, which makes use of Superspeed in a fistfight impractical because it requires him to use space to accelerate. But there is one use of Superspeed and Superstrength he uses quite well: a superspeed ram. Now this, he DOES do, on many occasions.
No such law of physics forbids achieving relativistic velocities in a single step, as you put it. It's all a matter of energy resources, and Pre Crisis Superman had virtually unlimited amounts of that. Even the energy he typically wielded to move worlds could easily reach so close to lightspeed that it's less than a trillionth of a percent less. Even the Byrned version who had power on the order of 40 megaton nukes at his weakest should have the energy resources to easily exceed 10% lightspeed.
Do not confuse speed as a single element or a one-dimensional power. Speed involves many aspects besides ultimate final velocity.
Solar sails can theoretically achieve near lightspeed yet no one in their right minds would try to win a race with one. That's because the
acceleration is so abyssmally slow for said sails. Ergo, acceleration is also an aspect of super-speed which Superman does indeed have which is also at a superhuman level. He clearly accelerates at superhuman rates instead of the mere 10 m/sec. peak human rate or else it would take him nearly a year to accelerate up to mere lightspeed -- when he's been clocked at achieving multilightspeeds for interstellar jaunts in a matter of seconds.
Reaction time is also an aspect of speed. Ultimate final speed may be irrelevant if others get the jump on you in reaction time. Superman even Post Crisis has been credited with nanosecond reaction times compared with normal human 0.1 - 0.2 second peak reaction times. To put reaction time in perspective, in the time it takes us to react, Superman would experience the subjective equivalent of over three years.
So, yes, he should be able to easily evade any normal timeframe attacks -- if the thought ever crossed his mind.
Though to be fair, Superman is after all, invulnerable; why expend energy dodging when it's just going to bounce off anyway? This is also something I've said of the Mighty Thor - why does Thor use his Hammer to parry bullets when his Asgardian bod's tough enough to make this attack ineffective against him? At least Wonder Woman bracelets, pre-Crisis, made sense in this regard: Wonder Woman wasn't bulletproof.
True and not true, sir. He's invulnerable to most normal attacks. But powers and power-levels rivalling his own can and do affect him. He can punch or pinch himself and feel it. So can Supergirl or Krypto when it comes to harming him. (Think about it along the same lines as a real world diamond being able to scratch another diamond.) Maybe he might be allowed some leeway for letting the first attack through out of invulnerability-habit. But it takes some pretty dense Kryptonian cranial matter to keep him from realizing he's under a harmful attack so he'd best do the super-dodge bit. The best I was aware of Pre Crisis was when he used his cape to help shield himself from an unknown weapon so he wasn't taking any chances; he'd have been smarter just to dodge the weapon in the human-timeframe foe's hands in the first place.
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