This conversion works.

It is important to work hard→To work hard is important.

Then, would this conversion work as well?

It's nice to see you→To see you is nice.


The first pair (to work hard) is okay. The second sentence of the second pair (To see you is nice.) is not used in (American) English. Why this is so is difficult for a native speaker to explain. The best answer I can give is: "It's just the way the usage has evolved over hundreds of years." The type of conversion that you describe is generally not used in English. For example:

It's nice to meet you. To meet you is nice. (The conversion not used.)

It's important to change the filter every month. To change the filter every month is important. (Conversion not used.)

It's good to hear from you. To hear from you is good. (Conversion not used.)