Not gibberish at all, in my opinion. They were carefully and creatively chosen, and derived in many cases from logical linguistic sources. I think it's just that we are used to milli- and micro- and nano-, but actual usage of "zepto" has been basically nil until now. But that will change.
On the other side, we're all very used to mega- and giga- and tera-, and for data center folks, peta- as well, and we'll adapt to the higher-order prefixes as they enter more common use.
Sure, but those are much smaller exponents than 21. I can see "peta" coming into use as storage sizes change, just as "kilo" has already disappeared from your list, but asking folks to keep track of 14 different prefixes is a little much. If it's outside of +/-9, I'd support the use of an exponent.
Remember that it's not 14 prefixes, or at least not 14 new ones. We're just talking about a couple new ones. There's only a new prefix for every three orders of magnitude, and everyone is already very familiar with the small ones. And there are mnemonics.
And we're not asking the layman to know all these, either. Zepto- will never be in common use; that's for particle physicists and basically nobody else, so far at least.
Everyone already knows 10^12=tera, so we're covered there.
±1 doesn't require a prefix, and while in Europe "deci" is used in common parlance for units of power ±2 it's not really used in scientific or engineering terminology globally. I'm also not sure what real quantity you're referring to which requires the power ±24 prefix (yes, the term "yottabyte" exists but no measurement of data capacity uses it).
On the other side, we're all very used to mega- and giga- and tera-, and for data center folks, peta- as well, and we'll adapt to the higher-order prefixes as they enter more common use.