Useful innovations are those which help society. Things that enable "standing on the shoulder of giants". Society values those innovations.
Often, the simple innovations are the best ones - yet, the simple innovations are also the ones most easily copy-able.
But, if something is easily copy-able, then one hesitates making those ideas public - for fear of copying and undercutting by competitors. Studies have shown that typically ~80% of R&D ends up as wasted effort (those 23 forks embarked on to realize #21 was the best).
So how can society encourage innovations to be made public? By providing incentives - such as patents - which are a limited time monopoly in exchange for fully describing the idea. Once the limited time monopoly expires, it is free for all - but in the meantime, others can read and understand the innovation - and either workaround (and provide society ANOTHER idea) or improve upon further or simply spark another idea.
Open societies out-proposer closed societies.