Think about what gets pasted into a word counter
A cover letter. A dissertation chapter before submission. A press release under embargo. A legal filing with a word limit. A resignation letter. A grant application. A novel excerpt going to an agent. These are drafts, by definition unpublished, and many of them are confidential until a specific date.
Counting words is arithmetic - it requires no server, no account and no copy. Doing it in the page means the draft is never transmitted and nothing survives the tab closing. That is not a feature so much as the absence of a feature, which is the correct shape for a tool whose entire job is to count.
Character limits are where the detail matters
Word counts are approximate guidance. Character counts are hard limits, and they are the reason people arrive: a meta description that gets truncated, a social post that will not send, a form field that silently cuts the end off, a subject line that turns into an ellipsis on a phone.
Whether spaces count is the question that decides it, and different systems answer differently - which is why both numbers are shown rather than one. A limit that says 160 characters and a counter that excludes spaces will tell you a string fits when it does not.
Reading time, and what it is actually for
Reading time is words divided by a reading speed, conventionally somewhere around two hundred a minute for ordinary prose. It is an estimate with a wide margin - technical material is slower, a list is faster, and nobody reads a web page in a straight line anyway.
It is useful anyway, as a proxy for whether a piece has outgrown its purpose. An article that announces twenty minutes is not too long because twenty is too many; it is a signal to check whether it is one piece or three that have been stapled together.