Why do /usr and /tmp directories for Linux miss vowels in their spellings?

Yup there were reasons. They are pronounced user and temp. passwd is similar, as is resolv.conf. Unix is an expert friendly, user antagonistic operating system.

I was a student when 300 Baud modems were the norm. I was the envy of my fellow students, since I had a Silent 700 terminal from Control Data where I was working. You could see the delay from typing each character and waiting for it to be echoed. Every character counted; I also see it as fostering the start of leet speak.

The hjkl from vi have a history which few know. vi was developed by Bill Joy when he was a grad student at UCB during these same years. The ADM 3a terminals in Cory Hall had arrow keys above those letters

They are holdover from Unix. Memory and disk space was in short supply. Hacking out a few vowels and other abbreviations gave real savings. A few disk blocks or a few bytes could mean the difference in being able to run a program or not. (I once had to trim a program by 24 bytes before it would run.)

Also as Tom noted terminal speeds were slow. 1200 baud was introduced as high speed and it was. I worked with one system that used a half speed teletype (55 baud or 5 cps) as the console.

On systems running graphical interfaces it generally doesn't matter that much as the average users won't be poking around in them. The directories are usually well documented in the hier man page.

Changing over to longer names would cause a lot of problems for existing programs. It would also limit script portability. Linking multiple names to the same directories would likely be more confusing than helpful.

EDIT: PDP-7 on which Unix was developed had a base configuration of 4KW of memory and a maximum of 32KW. Words where 18 bits wide. Input was a teletype, so speed was likely 110 baud or 10cps, roughly 100 words which is significantly slower than speech.

I'm surprised that nobody has commented on /user yet. This one is obvious: because it's not "user", it's "Universal System Resources".

As for /tmp, it's simply shorter and easier to type. C programmers have a habit of using short names when possible because they end up typing them many times in a program. It is very common have a temporary variable named "tmp" rather than "temp" for the same reason, you use "i" i for the index in a for loop instead of "index" or "counter".