[2022] Does the game write extensively on the disk while you play?

The only files that warframe itself will write on your machine during gameplay are

• The settings and profile (only when you make changes)
• Screenshots (only when you press the button for it)
• And the log file (usually not more than a few megabytes per hour)

Updating the game, which you need to do in order to play, will also account for some disk writes via the content cache however these are much less frequent

If you're seeing excessive disk writing while the game is active, I would check these first

• Are you running out of system memory, and forcing your computer to use the page file?  It's generally advised that you do NOT put your Windows page file on an SSD.  You can tell if you are running out of memory by checking Task Manager's "Memory" tab under Performance.  Installing more system memory will also probably significantly increase system performance in general.
• Do you have active screen capturing software running?  For example Nvidia's Shadowplay.  Depending how these are configured you might be writing significant amounts of video data any time a game is running.

You can also see what files are actually being written by going to the Start menu, and open Resource Monitor.  Go to the Disks tab, and then sort by "Total"  (bytes per second).  This will tell you at least what file/s are being written.