default_excetion_handler should log all errors

Why default_excetion_handler doesn't log all exceptions and errors into the PHP log. Printing them on a screen might be useful but it is hard to track errors triggered by a general user.  

https://github.com/moodle/moodle/blob/master/lib/setuplib.php#L374

https://github.com/moodle/moodle/blob/18aafd0ed4d89447cf7a6ac54c8aa7b710299563/lib/setuplib.php#L461

Why for example this stack trace which is really valid from point of site maintainer (error in custom theme) is not recorded?

My suggestion is that all exceptions should be logged into a log file?

Array
(
[0] => Array
(
[file] => /var/www/moodle/theme/ctufeet/layout/default.php
[line] => 22
[exception] => Exception
)

[1] => Array
(
[file] => /var/www/moodle/theme/ctufeet/layout/default.php
[line] => 13
[function] => write_course_data
)

[2] => Array
(
[file] => /var/www/moodle/lib/outputrenderers.php
[line] => 1374
[args] => Array
(
[0] => /var/www/moodle/theme/ctufeet/layout/default.php
)

[function] => include
)

[3] => Array
(
[file] => /var/www/moodle/lib/outputrenderers.php
[line] => 1304
[function] => render_page_layout
[class] => core_renderer
[type] => ->
)

[4] => Array
(
[file] => /var/www/moodle/course/view.php
[line] => 253
[function] => header
[class] => core_renderer
[type] => ->
)

)