Single-word requests are not the problem, they are just the kind of questions where some problems (in particular lack of guidance) predominantly manifest themselves. Only addressing these problems will lead to actual progress.
Some of the criticism described in the question is specific to single-word requests, but it is either not an actual problem or only applies to a small subgroup of problems.
The General Problems
The following problems are not specific to single-word requests; they are just more prominent in them. Banning single-word requests on their account would not solve these problems and we would get fed up with other question types soon. Rather we should address these problems in a more general matter.
Lack of Guidance for Askers
I think that many users asking single-word requests can actually produce good single-word requests if they receive proper guidance, preferably before asking.
Unfortunately, we do not have many ways at hand to provide users with guidance before they ask a question. Okay, there are tag warnings but they are broken. This problem is not specific to single-word requests; we see it with all sorts of questions. It’s not even specific to this site; on Let's Plan the Second Iteration of the Stack Exchange Quality Project!, the top answer and many more address this very problem. Instead of banning single-word requests, where this problem is very notable, we should lobby for a general mechanism to give askers guidance.
What we can do ourselves is give askers better and early guidance. As askers are not automatically informed about close votes (or even closure), we should help them with comments as early as possible. There was an attempt to create a repository for pro-forma comments, but it didn’t really take off. We really need some sort of resource for reviewers (and other power users) to make it as easy as possible for them to properly guide askers – not only for single-word requests.
Lack of Guidance for Answerers
Many of the above problems apply to answerers as well, however in addition I witness many high-reputation users leaving the following canned comment from the low-quality queue under single-line answers¹ for single-word requests (or the slightly modified one if the answerer has the comment privilege):
This does not provide an answer to the question. Once you have sufficient reputation you will be able to comment on any post; instead, provide answers that don't require clarification from the asker.
This is misleading as those answers are not proper comments. Moreover it does not provide any guidance whatsoever as to what is wrong with the question. We have to educate these reviewers that rather should not choose a comment and even better write a fitting comment themselves (or upvote an existing one).
Disposing of Bad Answers
When I obtained access to the review queues, I often skipped single-line answers¹ because I didn’t know whether I should flag them for deletion or not. Past discussions on Meta did not yield clear information, so I asked a question myself. Unfortunately many of the answers skipped one of the cases, but as a general tendency I would say that the community favours quick deletion.
While this outcome causes many reviews, these reviews are particularly easy. Single-line answers¹ on single-word requests can be clearly identified within seconds. So, I really do not see the reviewer and moderator load as a problem, as long as we all agree that immediate deletion is the best course of action for these answers.
¹ more precisely: answers without reference or other backup.
Answers in Comments
This wasn’t mentioned in the question, but this is something that annoys me about many single-word requests (and other types of question). These lead to long, unnecessary, and unproductive comment strings, loss of structure and quality, and they lead to moderation work.
In my opinion, this should be addressed by clearly banning answers as comments and agreeing that they are free game for flags. If sufficiently many users raise a non-custom flag, such comments can even be deleted without moderator intervention – but then we need to agree upon this. However, this should be discussed separately.
“I want this to be an expert site”
There seems to be a pattern on Stack Exchange sites (in particular language sites) that a group of high-reputation users wants them to be an expert-questions utopia. They want to gerrymander the scope such that it only allows for questions they are interested in. This is a bad idea.
As soon as a site has reached a certain popularity, it will automatically attract non-experts asking non-expert questions, and this is a good thing because it keeps the experts (who are most likely to ask expert questions) entertained. Moreover, while a single non-experts are less likely to ask expert questions, non-experts in total are more likely to do so due to their sheer number.
Unfortunately, not all experts are entertained by the same sort of non-expert questions, so most experts have to live with some non-expert questions they do not care about, be it single-word requests, questions on punctuation, or trivial grammar questions. If we want the site to strive we have to live with a portion of questions that we do not like. And the good thing with single-word requests is that they have their own tag and can thus be easily ignored.
Besides, I do not think that single-word requests are non-expert questions: Most of them cannot be answered with a dictionary or thesaurus (and I find it silly to require people to put a boilerplate statement that they searched a those, if it is not obvious what keyword they should look for). They need somebody whose vocabulary already contains the word – a feature most likely to be found on an expert.
Now, what can we do about all of this? Raise awareness and accept that we do not have to like every question on the site.
The Specific Non-Problems
While most of the problems with single-word request can be addressed and are not specific to them, there is some critique that I do not consider an issue:
The Guessing Game
These posts do not fit with the SE model. They are mere guessing games.
I beg to disagree. Of course, we can only make an educated guess as to what really helps the asker, but that applies to all Stack Exchange questions to some extent and at the end of the day, it only decides about which answer will be accepted, if any. What answers the question as posted is not a guessing game (at least for good single-word requests), can be evaluated by voters, and is useful to future visitors.
More than once, I was looking for a word and found it an answer in a single-word-request that was not the accepted one, because the question was about a sufficiently general problem.
While it’s inherent to the nature of single-word requests that answers are little more than a dictionary quote, I do not consider this a necessarily bad thing. The challenge lies in connecting this information with the question. Also, we are helping the asker and possibly future visitors.
“writing advice, programming advice, and shaming advice”
I do not see how this applies to more than a tiny fraction of bad single-word requests that should probably be closed. It’s not a problem of single-word requests in general.
Do not ban single-word requests in general.
Pressure Stack Exchange to give us some mechanism to inform askers and answerers before they post anything.
Install clear and easy guidelines for reviewers and other power users to reduce the reviewing workload.
Accept that each of us has to live with some questions that we do not particularly find interesting.