I happen to be an NVDA developer (although I don't write NVDA code in an active basis, I can answer some questions about it). Let me try my best to explain the situation so we can come to an understanding as to why I'm about to say what I will say regarding this issue:
Short answer: no solution unless developers are willing to get rid of an important thing that makes graphical user interfaces and accessibility possible.
Explanation: if I understand the issue correctly, the request is to turn off additional wording in document formatting such as "tree view," "alert," and others to make it more efficient for users. Yes, you can turn off announcement of things such as "tables," "links," and so on, more effective in web browsing contexts.
I'm sorry to inform you that you can't really disable announcements such as "alert" and "tree view." I think there is a bigger issue, and don't take what I'm about to say too harshly:
I think there is a confusion happening regarding format markers and control roles/types. This may stem from the fact that, in some cases (say, in web browsers), some things can be seen as both a format marker and a control type. For example, in web browsers, a link is indeed a control type, but it can be seen as a format marker (visually, a link is presented quite differently such as a different color compared too surrounding text), ultimately due to the fact that web content is based on document markup and other code.
Based on this, I think a much better way to explain the situation is turning off control type/role announcements. I can talk about a short-term solution, but before doing so, I must explain a high-level overview of how NVDA announces things like "alert" and "tree view":
NVDA can say "alert" and "tree view" depending on what software developers say what a control is. If the control (or something that is seen as a control inside a document in this context) exposes the right information about itself (through accessibility API's), then it makes sense for a screen reader such as NVDA to inform users as to what that control is. Doing so:
There are at least 140 control types defined in NVDA. Only a subset of them such as links, headings, frames, tables, and so on can be seen in document formatting settings panel because these are common ones encountered in various situations, most notably when editing documents in apps such as Microsoft Word and when browsing the web. This is because in addition to being a control type, these can be interpreted as format markers (heading in Word document, for example).
I think what you are really asking for is the ability to toggle control type announcements. There is an add-on "that will solve" the problem in a creative way (note the quotation marks): using sounds to indicate role (control type) announcements. We could perhaps say that we want an add-on or a feature change in NVDA to toggle control type announcements, and this is possible... no, wait, impossible, actually. Here's why:
What makes screen readers effective, or as some folks could say, efficient? If you think the answer is verbosity, you might be traveling on a road that could one day intersect with "screen reader street." If you think screen reader features, perhaps you might be walking on a street that may or may not intersect with "screen reader street." If you think it is reading different screen content, perhaps you might be standing very close to the "screen reader street."
I think what truly makes (or breaks) screen readers is not verbosity, features, nor content reading. It is information accuracy in a vast ocean filled with possibly conflicting data. Information accuracy for screen readers is informed by choices made by humans:
One important information gathered when working with a control is its role (control type). Depending on how the screen reader processes it (or perhaps announce or not announce it), users will get different experiences due to changes to information accuracy:
To sum up the discussion in front of me: NVDA must navigate an information ocean, striving for information accuracy while acknowledging information blackout. Control type announcement happens not at the speech level, but at the level of accessibility API's - whatever the pap says what the control is, that's what the accessibility API will say, and from that moment NVDA will say whatever it is told to say. People can change things here and there such as turning off announcements of format markers that are control types in their own right. But consider: there are times when efficiency makes sense, but for this issue, it affects information accuracy.
The point I wanted to teach people through this lengthy response is that, although suggestions such as turning off things to make the experience more efficient sounds fine, but when you think more critically about it, a feature request such as this one may not be feasible. More bells and whistles (including silencing some data) could decide the reputation of a screen reader, but they cannot surpass the bigger picture of accurate scales and weights (don't forget about measurement units, and for some, impact of gravity). So my honest opinion about the feature request to toggle control type announcements: more harm than good (sorry; note that this is my opinion so it does not reflect positions of other developers).
Hope this helps a lot.