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I'm questioning the usability of it (perhaps I could use the title attribute "home" but at the moment I have hundreds of pages with the keyword "home" pointing to my home page and I wonder what effect i would see?
Would I risk current positions and even supplemental for such a site wide anchor text change to an important page?
I renamed a link going to my "Main Contents" page a few months back. It was descriptive to humans, but to SEs I felt it didn't really indicate the true nature of the destination page. So, I changed it to "Main Contents" and did it all at once.
My site has been in an up and down mode ever since. I'm not sure if the link anchor text change made any difference, but I'm thinking it didn't help either. If I had to do it over again, I would have done 10% of the links, then waited for those pages to get cached, then do another 10%, etc. Who knows, at some point you may actually determine there's a benefit to not having them all have the same anchor text.
"Would I risk current positions and even supplemental for such a site wide anchor text change to an important page?"
Appropriate link text will help you, and pages don't go supplemental due to link text for a page.
The only way that you could face a problem is if you are "only" changing this - in other words NEXT TIME YOU ADD CONTENT make this change. Do not just change the alt tag - add to the site as well images, words, etc.
Is a webpage made of supper thin glass ready to break at any change?
I think this is a great quote.
While there's certainly nothing wrong at all with asking questions and learning from the experience of others, there are a lot of variables at play on any given website. The only real way to know is to try.
If you are not that aggressive yet it may help, but if you were already quite aggressive with your anchor text and your link profile is somewhat unnatural I probably would not push it too hard (or if you do be ready to change it back if it causes bad things to happen).