Languages are expressed in any of a wide variety of writing systems, each of which use one of at least five general mechanisms:
In a logography, symbols correspond, roughly, to words. Uncommon or complicated words correspond to multiple symbols. (Many logographies have many more details I'm leaving out here.)
Logographic writing is compact. Thus it takes less space, which is helpful in many small obvious ways. You can also write it quickly, tho this is limited by the complexity and error-intolerance of the exact system. This can easily reach the point of writing as fast as you can think.
The main benefit of logographies is roughly the same benefit as you would seek in a shorthand system. Logographies, however, tend to be more error-resilient than shorthand.
The main problem with shorthand is that you don't already know it, and must usually take great effort to learn it. You may already know a logography, making the learning just a matter of relatively-trivial practice and frequency. (Tho if you're reading this, you're probably an English speaker, and not that likely to already know one.) Learning a logography can be useful besides as personal shorthand, for logographies usually correspond to languages used by many others.
You may be thinking of Chinese or Japanese as the main example of a logographic language. This is reasonable, if you haven't looked in the right places. You may object
You're telling me to learn Chinese/Japanese so I can write faster? Learning a full language is harder than learning a shorthand system, and those are especially hard for most outsiders. No way this is anywhere near the best method.
If that objection isn't salient to you, go ahead, try logography, and skip this section.
Otherwise: this is where toki pona gets way more useful than you thought.
Toki pona (literally "good language") is a deliberately extremely simple constructed language. The number of words isn't clearly defined, but it's somewhere between 100 and 200.
Yes, you can get a fully-functional language out of so few words.
From that brutal simplicity, it happens to be perhaps the easiest language to learn to the point of general usability, possibly ever.
And it has a logography, "sitelen pona", which actually follows the one-symbol-per-word ideal. You can express the entire logography on one page, maybe double-sided. Most of the symbols are simple and hence quickly written.
Minimalist language designers accidentally made the perfect shorthand.
To compare the compactness of a few writing systems, I wrote the same few texts (translating as appropriate) in each one, and measured length in notebook lines. (You can see some of the exact texts here to compare for yourself.) The shorthand I used is a personally-modified form of Dutton Speedwords.
For the lyrics of "kulupu jan tenpo", a well-known toki pona translation of a song:
That particular text is biased in favour of toki pona. I tried to compensate by keeping the English concise and vague.
Often, us two are beside each other. / This is the only path thru time. / You love brokenly, and go down. / But you keep feeling good.
In breaking, you stay on / your path, and clean up. / Know this: / Bad doesn't end. / In badness, hear this:
Fly! / Do everything! / You can, to me! / I can hear / your sound / from my heart.
Fly / in the sky! / Feel the sun! / In the future / we're in the wishes of / generation.
pakala la, sina awen lon / nasin sina, li weka e jaki / o sona e ni: / ike li pini ala / ike la, o kute e ni
o tawa waso! / o pali ale! / sina ken, tawa mi! / mi ken kute e / kalama sina / tan insa pilin mi
o tawa waso / lon sewi laso! / o pilin e suno! / tenpo kama la / mi lon wile pi / kulupu jan tenpo
For a quote from Max Planck ("A new scientific truth does not triumph ..."), with some simplifications and concisions to the English to reduce bias:
New science doesn't spread by convincing opponents. Rather, its opponents die, and the next generation grows up familiar with it.
For the opening lines (as approximated from memory) of The Oldwood (a friend's unpublished philosophical novella, discussed previously):
You will never know my name. You will know me as The Oldwood — or otherwise, you will know me as Evan — but you will never learn my surname, or if I had a surname. In this book I will be Evan for the first half; then, via some miraculous transformation, you will find that I have become The Oldwood.
Dutton Speedwords, the basis of my shorthand, may be on the inefficient/robust side of shorthand systems.
For further comparisons, look at my documents translated into toki pona: