Do we really need gold open access if publishers permit self-archiving and sharing? Several well-established journals nowadays allow self-archiving or sharing of articles through an institutional repository. For instance, Elsevier allows immediate sharing of the accepted manuscript via the author’s non-commercial homepage and, after an embargo, through their institutional repository. Springer has similar rules. More in general you can check on Sherpa/Romeo for any journal’s policies. 

So I am wondering: is it worth it paying for the open access option, when we can just choose our publisher wisely, and then prepare a nicely formatted version of our accepted articles to share them online?
What you're describing is open access. It's simply a different form of it to the one Springer want you to pay for...

There are effectively two-and-a-half routes to open access, with a lot of subtle variants between journals -


Gold - the article is available immediately, freely, and in perpetuity, via the journal's website, probably with a permissive copyright license. The big open access journals (PLOS One, Scientific Reports, etc) are generally all-gold. It is usually paid for, but not always - many journals are gold but don't charge.


Hybrid gold - a special case of the above but for a single article in an otherwise subscription-access journal, rather than an all-gold-OA title. Usually costs more than an all-gold journal and almost always paid for.

Green - a version of the article (usually but not always the accepted manuscript) is available through a repository (or personal website, etc), often after a delay of around a year, and usually without a permissive copyright license. Usually no charge (other than standard publication costs if relevant).


Almost all mainstream journals allow green open access, though the rules are complicated, and they often refer to it as something like "permitted distribution" rather than "open access". Most journals from the big commercial publishers offer hybrid open access, though exactly how common it is for people to take this option is still a bit of an open question. (Finally, most all-gold journals also permit green open access, but obviously it's less important in that case!)

So, the question becomes - assuming my journal allows green OA, as almost all Springer and Elsevier titles do, what is the point of paying for hybrid? (This is a question I answer a lot for people looking at OA option forms, and most of them decide not to...)

Possible reasons to take gold over green, assuming you've already decided on committing to that journal, might be -


Audience. If you expect the title to be of wide public interest (= lots of non-academics want to read it) or valuable to particular audiences in regions without great journal subscriptions (Africa, South America, etc) then hybrid gold may make sense.
Timeframes. If you know it is likely to be of particular interest now, and making it publicly available a year or two down the line would be much less valuable, for whatever reason, then hybrid gold is more useful.
Distribution. If you know you'll want to make a lot of copies of your paper and distribute them widely and publicly, having a permissive copyright license through hybrid gold may help do this.
Discoverability. Hybrid OA papers are marginally more discoverable than green OA ones, as you can find them through the journal website, the DOI points to them, etc. A repository or personal website may not always be as easy to find.
Policy requirements. In some cases, funder or institutional policy will require that a hybrid OA option be taken if available. This is rarer now, and most of them are starting to pedal back on hybrid spending, but it may apply.


In practice, most people don't take the option. And if you want those specific benefits, you can get most of them from using an all-gold OA journal in the first place...