You can allow your copy of HTTPS Everywhere to send us certs, which can help researchers understand what CAs are doing and potentially detect misissued certs.
Two other important mechanisms are Certificate Transparency and HPKP.
The former is a way -- I hope! -- to eventually require the open publication of all issued certs that the public is expected to trust. The latter is a way for sites that you successfully connect to at one point to prevent other CAs that they don't have any relationship with from helping to MITM your future connections.
For the answer to what SSL has to do with certificates in the trust store, the best demonstration is by example. Try to setup mitmproxy on EC2 to MITM your own HTTPS connections. In order to do so, you will need to install a trusted root certificate on your device.
Why are there 200 root certificates in my Apple key chain? That is at least 200 entities who can MITM my SSL connection without my knowledge.
The trust assignment protocol is a vital aspect of communication security. What good is end-to-end encryption if I don't know which "ends" to trust?