Not necessarily. There are an unlimited number of algorithms available to implement any particular concept so people are always looking for faster, more efficient algorithms for implementing the same mathematical concept.

However, the marginal value of doing the R&D to find additional algorithms diminishes as more are described even if they all are patented. This is not a side effect of patents per se but a side effect of how algorithm research works.

Companies often spend millions of dollars on the computer science R&D required to generate a new algorithm so there is a return on investment calculation. For the R&D to be worthwhile, they either need to produce an equivalent new algorithm for less money than licensing it or believe that they can find a materially better algorithm than the current licensable algorithms such that they have a market advantage. It is very similar to chemical process R&D.

Not so much in academia. But yes, this would hamper or delay practical/field deployment. See EC crypto etc.

ECC is widely used in industry. DJB seems skeptical of its patent encumbrances:

http://cr.yp.to/patents.html

I do agree there was a time when ECC patents were an issue (particularly Certicom's), but it was certainly not as big a deal as the RSA patent.