you think middlemen inject themselves into transactions that don't require themI'm responding more to this (and more as a general concept).
If given the opportunity, people would do this. So it's useful to dispel the notion that because its "not seen" it's not a problem. It might not always a be problem, but many it is and others it's also "annoying".
Stepping outside of markets for a second, this is why M&A deals have exclusivity and breakage terms. The theory/practive on why you do this involves assymetric information and something economists refer to as "opportunism". Opportunism[1] is exploiting legal abiguity for narrow self interest.
The more complex the legal/transaction structure the wider the attack surface for "opportunism" (because it's proportional with deal complexity). In slow and complex deals like M&A at a certain point it becomes an issue and so safeguards are taken.
In fast and simple deals like buying stock on the box or what not, the scope is very limited. The glaring example is the broker issue you highlight. But as the deal structure gets more complex, this risk rises.
Now, the attack surface for opportunism is proportional to deal complexity as mentioned above. This is legal/structure but also now needs to consider execution and # of counterparties. Limiting counter-parties (ie, middlemen) reduces this "attack surface" (if you will). Because each of them needs to be monitored/paperwork delath with etc. This is why such uncecessary interventions are structured out of deals. Typically by way of convention/courtesy if not expressly by things like ethics codes & stronger (ie, exchange regs+laws).
This is a long way of saying that the institutional integrity of markets hides a lot of problems. This is a good thing. But not to be taken for granted. The cost of undermining these institutions/trust etc. is not insignificant. Because it means you have to solve all these problems again in new ways.
[1] https://en.wikipedia.org/wiki/Opportunism