You won’t have zero, the Nats will make him a Qualifying Offer, the draft pick they receive if he signs elsewhere is probably equivalent to what they will get for him if they trade him at the deadline.
Meanwhile to the average Nats fan, all they are going to say is “oh my gosh, they traded away Bryce!” The optics are much different if he decides to walk in free agency.
Letting him walk for nothing isn’t something that can happen.
Well...it's complicated:
Under the new rules, since the Nats aren't a revenue sharing team, if we let Harper walk we get a pick in the "B" round of the compensatory draft, after the first round, and after the "A" round (which are teams who lost QO players but receive revenue sharing).
But wait, there's more - if the Nats go over the luxury tax threshold this year, the compensatory pick will be after the 4th round (we were over it last year).
Whoever signs him would surrender their second highest draft pick, so that could be a second rounder. If it is a team that's over the luxury tax cap, they would surrender their 2nd and 5th highest picks.
So it is entirely possible that if we let Harper walk, we get a 2nd round pick (and maybe a low one if it's Chicago or LAD that signs him), plus a pick after the 4th round (and maybe a 5th rounder). Given that, it arguably makes more sense to try and deal him before the trade deadline if we are out of contention and not likely to resign him.