You are quoting from Wikipedia and that quote is an oversimplification.
If you redefine the law like that, then sure, I agree that there are many uniform distributions too where the 1st digit is likely to be small. Here is another simple example: Consider the distribution of positive integers from 1 to 2. If we pick a number at random from {1, 2} then the 1st digit is likely to be small. This kind of analysis is boring.
But (fortunately!) that's not what Benford's law says. Benford's law provides a specific formula. Check https://en.wikipedia.org/wiki/Benford%27s_law#Definition to see the specific formula that must hold good for a set of numbers to be said to obey Benford's law. That's what makes Benford's law so interesting whereas your example ranges are degenerative cases where nothing new, surprising, or interesting is going on.
If you redefine the law like that, then sure, I agree that there are many uniform distributions too where the 1st digit is likely to be small. Here is another simple example: Consider the distribution of positive integers from 1 to 2. If we pick a number at random from {1, 2} then the 1st digit is likely to be small. This kind of analysis is boring.
But (fortunately!) that's not what Benford's law says. Benford's law provides a specific formula. Check https://en.wikipedia.org/wiki/Benford%27s_law#Definition to see the specific formula that must hold good for a set of numbers to be said to obey Benford's law. That's what makes Benford's law so interesting whereas your example ranges are degenerative cases where nothing new, surprising, or interesting is going on.