As Stephen and Maximillian mentioned, search engine algorithms don't take into account whether a post or a page has an image on it or not. Now, yes, someone may discover your site through image search or share the image on social media. Also, a relevant image with good alt text and caption may raise the relevance of the page. But having or not having an image on a post is by itself not crucial for search engines to rank you.
Also, keeping in mind that search engines still ultimately look at relevance and popularity when ranking content for search queries, the actual website traffic is not a factor. It is only a factor when users come to that website via a relevant query. But you can have a junk website with loads of random (mostly bot) traffic that won't actually rank for anything, for example.
To answer your question, everything in your posts and pages should be relevant to the user. That includes images and their metadata. So you're better off tailoring images to your pages.
Now, there's nothing wrong with having a default image. For example, if someone shares your post on social media, it's better if an image (such as a company logo, or a photo of the website's subject) is present, since users do still click more on content where an image is present. However, using the same image with different alt tags or captions will be awful for users, and this manipulative behavior may even get your content devalued, if this is abused 99% of the time.
I would advise you to use relevant images and metadata whenever possible, and if you do have a default featured image, pick the best metadata as it relates to your website's overall purpose and stick with it.