In the first issue that you cited, sipa said that the core maintainers do not, and do not want to decide what the network's rules are. By this logic, they would be unable to merge any kind of forks into the Bitcoin Core code at all, including soft forks. Additionally, they seem to be threatening to HF a change in the PoW if the miners do not accept SW, which implies they are both able to change the network's rules in regards to the PoW, and are saying that SW is something that needs to be part of the network's rules.
Are you honestly implying core has a set of magic rings that changes the consensus rules of the network by touching them together?
The network has to accept them.
Core can't unilaterally do anything meaningful but accept and reject proposals to the network/system.
Core has significant influence, a big part of this is because what is merged into the code by Core is advertised on the same website that the Bitcoin whitepaper was originally hosted on, and in the forums that satoshi posted in.