Good question. You could do that, but you’d have to add in what Ray’s and Book 2 doesn’t have that’s in Mathematics: an Instrument for a Living Teaching…
Like Ruralmama said, Book 1 gives the child time to explore and make friends with numbers through 100, allows children time to gain ideas before memorizing facts (though +/- facts are often learned during Book 1 due to the mental math work). Even the number 1 has an idea attached to it and there are many other ideas a child receives in Book 1, perhaps one of the most important is the idea of place value.
For more information on why Book 1 is important, you might enjoy in particular The Life of the Math Lesson, which goes over more of the ideas found within.
Let me know if you have additional questions.
Richele