It sounds like you want something that works the way it does for example. asked Jeremy. Ie, just some long list with each image and its alt attribute. The problem is that this will not give you enough context to provide the useful alt attribute, because the alt attribute should not (in general) βaccurately describe [...] the image that they represent,β but rather describes that the image is intended for views on the current page. It is difficult to give a brief description of how to write useful alt texts. The Wikipedia article on alt attributes by itself sucks the current state in it, but the links are useful. There are, of course, many other SO questions related to this.
Maybe some kind of pre-written tool that does what you asked for, if, for example, all pages are reachable from the start page, you could just scan the entire website and generate a list. But if it is possible only on some pages, for example. the search may need some kind of tool to work with the site.
In any case, let's say that we have such a tool. Even then, its use is quite limited. Even if you can get a list of all the images on a website using the alt text associated with it, you still have to visit all the pages, one page at a time and, possibly, use some web developer extension in some browser (there is such tools in other answers, I think), which displays all the texts on the page; and then correct the alt text after you know which image is actually used on the corresponding page.
So, this tool that you request will be useful only for searching pages with possible improper use of the alt attribute (that is, any page with an image on it). (But depending on the site in question, even this may be useful, of course.) You still need to open a web page that actually uses the image (or, if you want, read the HTML code for the page) to find out which one will be correct / best text.
So, at best, you get a list of pages with images that you should check. But it will still miss some important cases, for example. cases when the CSS background-image property is used to display a button (instead of an img image), which should have alt text.