Are there examples of more efficient funding systems than grant applications?
Of course. Remember that in many countries, institutions get a lot of money based on solely being. As an example, in the Czech Republic, the Czech Academy of Sciences receives a lot of budget money for its operation, and some of the money is of course used "for research". Just as an example, until recently, almost all employment expenses (salaries, offices, building maintainance, etc.) was covered exclusively by budget money. Similar model exists in other countries, for instance in France with CNRS, but the difference is that most CNRS people are associated to particular universities, just without teaching duties.

It works well because you moreorless know what you get. Financial stability helps in establishing long-lasting projects etc. Of couse, some level of control is necessary so that good people get the money. In the Czech system, this is based on (AFAIK 5-year) audits which evaluate each person separately, and then whole departments, working groups and institutions.