At least since MediaWiki 1.26 there have been a lot of reports in Support desk for problems with a temp directory
Since rMWb7e65e555adc2b77dad55eb2b28338bf2e7619e1 things should be improved, but still, PHP is_writable() function may not catch ACL permissions, SELinux and the like. The installer should not only rely on wfTempDir() but also actually write a temp file on it for testing this functionality.
I think doing this test during the environment tests and return a big warning, would prevent frustration on people installing MediaWiki for the first time that experiment this issue. The error happens usually in load.php so it may not be obvious where to look at, since there's no visible error (unless one looks at the browser's error console, which is not a common place to look for system admins and general users)
I don't think aborting the install should be necessary, since $wgTmpDirectory could be set after the install.
Examples of such problems reported: