textutil does not respect -font or -fontsize parameters

Hello.

I'm having a problem with text files with small text being exported from an application and some scripts that I use. Since the number of files is large and I often use the script, I don't want to change the font size by hand in each file, so I looked up textutil, and tried the following in Terminal:

textutil -cat rtf -font Avenir -fontsize 16 -output combined.rtf *.rtf

A file combined.rtf with the contents of all the original files concatenated was duly created, but the font was Times and the size was 12. I tried again with different fonts and different sizes, but everything resulted in Times 12.

Am I using these parameters incorrectly? Is there any way to increase the font size using textutil or something else?

Thanks for any help.

OS X 10.10.4

MacBook Air (11-inch, Early 2014)