When it comes to SEO, I often meet two types of webmasters. The ones that know nothing about how search engines work and the ones that obsess over the smallest SEO concerns. There is often never a balance. :)
That being said, there is a fun Google Webmaster Help thread where Google's John Mueller basically said it is more important to build an awesome site than to focus on every little technical SEO aspect of your site.
Of course, if your site is not indexable and has major SEO issues, you need to focus on that. But beyond that, focusing on the text in your alternative text over making sure you have the best site for your users, might not make sense.
Instead of focusing too much on technicalities, I'd really focus on making sure that your site is the absolute best of its kind. Resolving technical issues is always a great idea, but it's really even more important that your site itself is overall awesome.
Now, generally this makes sense. John is of course talking to a specific webmaster about a specific web site.
But generally, if you have an awesome site, Google will want it to be indexed and ranked. If you don't and never will, then brute-force your technical SEO to squeeze all the ranking juice you can. :)
Forum discussion at Google Webmaster Help.
Image credit to BigStockPhoto for super hero