I suggest reading this wiki page:
https://en.bitcoin.it/wiki/ScalabilityThe 7 txps limit is arbitrary, not a design choice, and can be increased quickly if necessary.
Miners won't suffer from this - they only have to confirm each transaction once per pool.
Quickly may not fast enough if it takes several weeks to implement as the wiki page said. And the miners must make changes so they can process larger blocks, which too may take a while for them to implement.