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Yeah very true, I agree with this take.
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I'd probably caveat your statements by noting that Caesar was an avid self-promoter and built up a cult of personality around himself. Without a doubt, he was a brilliant, brilliant man ... but given that he was the first in a long line of dictators using his name for legitimacy, I think it's rational to bear that in mind when reading glowing Roman accounts of how brilliant he was.
Powerful men with a desire and incentive toward self-aggrandizing can often be successful in building a tremendous amount of personal mythology. e.g., a few years ago Elon Musk had millions of people willing to claim he was a genius, an accomplished engineer, a marvelous rhetorician, etc.
With all that said, some rebuttals for Caesar, specifically:

Engineering. Caesar's decision to build a bridge across the Rhine was certainly militarily intelligent, but his bridge wasn't novel; the design had existed for 500 years by this point, and was the same design as was employed for the Pons Sublicius, the oldest bridge in Rome. Additionally, it's worth noting that Caesar was accompanied on his Gallic campaigns by a quite famous chief engineer (praefector fabrum) named Lucius Balbus. Which of the two seems more likely to have come up with novel engineering concepts?
Literacy and Rhetoric. These weren't particularly different skills in ancient Rome. No disagreement that Caesar was a phenomenal communicator ... but then again, most truly memorable politicians are, aren't they? One note, though ... reading silently was an unusual way to read, and was more odd / impolite than a sign of genius. It indicated that you were concentrating on the message so hard you forgot to read it aloud.
Explorer. What you're highlighting is also an extension of literacy / rhetoric. Caesar didn't explore places other Romans had never been ... instead, he provided lots of gripping details about his campaigns to ensure Romans believed his (self aggrandising) accounts. That didn't require him to be particularly truthful about the people he encountered, and much of his writing is out of line with historians of the era (e.g., Livy disagrees with him about population counts, territorial dispositions, etc ... and is more in-line with archaeological evidence). Even Caesar's friends and subordinates questioned the accuracy of Commentarii de Bello Gallico.
Furthermore, in no circumstance did Caesar travel / explore farther than other Romans, and Romans themselves didn't explore so far as, say, the Phoenicians. We can certainly wonder if Caesar made it to Denmark in the 50s BCE... but we know the Phoenicians did, 800 years earlier.
The Caesar Cypher. This is named after Caesar because he's famous, not because he invented it. Suetonius (our source for him using it) didn't say he'd come up with it, either -- just that he used it. It'd have been odd if he invented it, because transposition ciphers were 1,500 years old by that point, and both the Hebrews (in around 500 BCE) and the Greeks (in around 300 BCE) were using similar, but more secure, cyphers.

To boil it down... what you've described is a man with an incredible military mind, extremely literate, and a consummate politician ... but not someone exceptional as a scientist, artist, musician, explorer, astronomer, philosopher, etc. ie, you've described someone who isn't really a polymath at all.
Compare Caesar to say, Benjamin Franklin. Ben certainly wasn't as skilled of a military strategist, but one could easily argue that he was:

Just as good a communicator and writer
Accomplished (in his own right, not for an employee's work) in engineering, practical philosophy (see: numerous list of inventions), mathematics, statistics, chemistry, business, and political philosophy.
A talented musician, a serviceable composer, and a habitual illustrator >

I agree with most things here. But come on… you can say Elon Musk is accomplished / intelligent while also disagreeing with him or thinking him the devil himself. Not everyone who is your ideological enemy has the capacity of a toad. >

That's not the point -- I think Musk is great at hiring intelligent people, had sound business sense for most of his career, and is an incredible promoter and salesman. What he isn't is an engineer or inventor... By inclination, education, or professional experience. 
And yet, you get articles like this from a few years ago, which work on the fallacy that being an accomplished executive in several fields requires you, yourself, to possess all the individual skills necessary to succeed in those fields.
You don't -- any more than Caesar needed to be an accomplished engineer to benefit from accomplished engineering.