Salary dump. Frees up space for them to also get Heyward. They've been linked to him.
Would be a great top 7 for any team
That would be wonderful if you had Gardner 2 or 3 years ago and Werth about the same. They're 32 and 36 (37 in May). That's only a decent defensive outfield and probably not a good one offensively next season (how does it even align? Gardner in CF? Heyward? Does Heyward or Calhoun play right?), a problem that could be easily solved by not trading Mike Trout.
I can't see why they'd want to give up anything of value to get Werth. He'd be a DH on that team, probably not a good one, and definitely a very well-compensated one. The only way the Nats can dump Werth is by either eating salary, packaging him with someone useful for not much in return, or a mix of the two. Look at it another way: Wilson and Werth are both declining assets who are overpaid, but Wilson only has one year left on his contract. Gio is a slightly above average SP with one year left on his contract; Wilson is a slightly below average SP with the same. Gardner is a 32-year-old speed player who's losing speed, wouldn't hit home runs in Anaheim, and can't really play CF any more.
You're offering a slight upgrade on CJ Wilson, plus a 32-year-old corner outfielder with power that doesn't play in their stadium, plus an overpaid DH, plus an oft-injured (but good if he stays consistently healthy) player with 1 good season under his belt, for one of the best players in decades in the prime of his career and some salary relief.
Think about if Rendon played for the Yankees: now see them offering the Nats Rendon, Gardner, Teixeira, and Carlos Beltran for Zimmerman and Harper. What would you say to that if you're the Nationals? (Probably nothing, as you'd be laughing too hard.)