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I'd say it's the opposite. Big companies can afford to take a shot on someone and miss without materially impacting the business.
If I'm hiring developer #2 at my 5 person startup, I want someone confident and cool under pressure who has done something similar to what I'm building so many times in real life that the coding test is a cake walk.
A dev hire on a small engineering team (< 5 people) can make or break the business. I'm trying to de-risk that hire as much as possible. I want to design a test that 90% of people will fail so I can find that top 10% developer.
Once I get to 15-20+ devs, I'm much more likely to relax my criteria and look for a diamond in the rough.