... accepts broadcast transactions that come along but also constructs a new block from its mem pool on top of it according to his own rules, and broadcasts that new block.
This is actually the job of mining POOLS. Individual "miners" are most probably hardware owners, that sell their hash rate to mem pools, to mine on the blocks that the mining POOL constructed according to its very own rules.
It is really difficult to find a block. It is really, really difficult to find a block. It is the individual miner that finds the block. My miner could find a block. In fact if you check out
https://kano.is/, the pool broadcasts who finds the blocks.
Bolck by bapir with 78TH/s! Welcome to the Acclaim Board with your 1st Kano block!

That's number 3 for
BLOCK FRIDAY!

S9v2

Note the S9v2. That means it is a newer S9. A person who bought one of the miners found a block and shared it. S/he could have kept the entire block reward. People solo mine with older equipment, like S3s and such. Whenever it is "unknown" it's probably a solo miner. Good on them! Most of the time is a larger farm though that has the ability to game.
Meanwhile, the more hashpower = more security = larger market investment =

Bitcoin.
It is genius. Nobody can force their will on others. It takes multiple agents.
These nodes are the only "source of block chain". They send out the originals.
Yup. That's why I run one, but I don't solo mine because the
odds are so small of finding one block. It would maybe take 6 years. It is the individual miner, computer, that finds the blocks. Because the odds are so small, people pool their hashpower and
work together. It is genius to have division.