I've hired hundreds of people and this is just not true. A first impression matters a bit, sure - but it has hardly any effect on the decision.
> There is also the reality that when companies need to fill a role, and when first start interviewing they will set the bar way too high and reject some perfectly qualified candidates
This is a very poor hiring practice. You should what you're looking for and what you are willing to pay for it. And then you should recruit a candidate pool that meets this criteria and go from there.
Hiring is literally the most important job a manager has in any fast growing company. It should be taken very seriously and systematically.