WordPress has custom fields in core.
They are just not advanced, but they are there. It is generally known as user_, post_ and term_meta.
You can add, display and else manipulate them either in the GUI or with code.
It also has a very advanced options and settings API, which is what is to be used for “Theme level” or other types of settings/options.
Posts and pages are as said already covered under the fields available in CP.
For more advanced fields, say select or repeating or else, Core can not implement this because the ramifications and wishes are endless. Would it implement a select, someone would ask for select2 and the other for bootstrap and the third for ajaxified load of options, just as example. So this is where plugins come in.
That is, thus, a job of plugins to offer more advanced options of custom fields (which unfortunately are rare in CP)
That all said, there is a petition to advance the Fields API more, in core, see: Finish the Custom Fields API