Can't we use our processing power more efficiently, both by mining coins and helping in university research. I'm sure people should be able to buy up processing power.
The processing power is used for security. It makes it very expensive for someone to undo previous transactions.
You need a problem that is very hard to solve but very easy to verify that it was solved correctly. This is called "proof of work". SHA256 works well for this but the work isn't otherwise useful. Folding@home, SETI@home etc don't have the right properties. They're hard to solve but it's hard to prove they were solved correctly without doing all the work over again. Most if not all research problems will be this way.