How is a number like 73,000,000,000,000,000 more challenging to write and comprehend than a number like 73?

Because the number is bigger... and takes longer to write and read.

Because the first number is so huge. We can have a fair idea how big 73 is but its  almost impossible to appreciate the magnitude  of that first number. Also its easy to miscount the number of zeros when you are writing it.  

Numbers as big as the first number are best written in scientific form this one would be written as

7.3 * 10^16   - much easier to write this!