TL;DR: We certainly don't need it. It has no point.
It's a meta tag, one of the bad ones
It is irrelevant to the question if my own Sprachgefühl, Microsoft Word, the editor of my novel, a teacher or the pattern answer of some certificate or English test triggers my concern about a sentence or wording. It can be in the question, but it's not worth a tag.
The result is the same, the people come here and post a question. Neither of the tags, homework, test, gre, cloze-test, microsoft-word and spelling-checker adds any valuable information to the question. On the contrary they are likely indicators of bad questions with little research.
If the tag can't work as the only tag on a question, it's probably a meta-tag.
Neither of those tags can stand on their own. They do not indicate anything about the question. Is it about a word being not recognized? Is it about a sentence structure the program didn't recognize? A printing error in the text book? A strangely worded test question? Nothing. Those tags tell us nothing.
They don't us anything about the type of problem, about the parts-of-speech or linguistic field involved and they don't help us to put it in a general area of expertise like the tags for other sciences, languages and time periods do.
Those six tags are the embodiment of the taxonomy mess on ELU. The meta tag rule is from 2010. In August it had it's sixth birthday. Maybe it's time to give ELU a present commemorating that.
The usual solution: blacklist them all
If we truly deleted those six tags and blacklisted them. Everyone trying to ask a question with those tags would get a warning before posting. This could very well be the relief of shitty test questions that is so often discussed in chat and part of so many meta discourses.
The warning would look like this one:
Why we don't do it
At ELU, we are unable or more precisely unwilling to do it. Having a meta discussion about tags makes people apparently ignore it. It took four years to blacklist the tag words. If we look without any further analysis at the posts tagged tags they have comparably meager up votes and few answers. ELU people just don't care enough to voice a proper consent on anything tag related.
It's not like they have low up vote counts because they are disputed. The few I randomly checked have no single down vote. There are just in total only a few up votes. It's just that nobody cares. Since the community managers for good reasons can't take apathy as support nothing changes as long as we don't have enough voices to show proper support for our tag measures.
Unfortunately until that changes we will mostly be stuck with our own continuous re-tagging efforts. Blacklisting is done one a StackExchange permission level above moderators. We as ELU participants have to show via voting on meta posts that we have a consensus for them to act.
We have only a few people who suggest tag measures and only a few more people to show their support for those measures. Here is the pitiful voting pattern for the blacklisted word tag question. It got five votes in the first two times it came up. That is for a tag that has been "has been heavily discouraged since the early days of the site." As such I would expect the full voting weight of the moderator team and site regulars of the time behind the proposal. Not sure if that really only amounted to five back then.
Maybe there's some light at the end of the tunnel. We have a new moderator who cares about tags and my question regarding the language tag has garnered 13 up votes in a week. That tag is in the same ball park of ridiculousness as the words tag was. Maybe that's a good sign.
If you do want to start getting rid of those tags, this is the way to do it.