First off, if you let Hayward walk, you have just fired yourself and Snyder, because you won't win many games the next two years.
Now, you decide to let Hayward walk. Then what do you do? Resign Jefferson, Marvin? Go after someone like Granger? How do you fill the SF position? Or do you let Hood be your starter and go after someone like Garcia to play SF?
If you go after Marvin, Jefferson or Granger, you are going to have to pay them close to 10 million on a 2-3 year deal. If you sign Marvin or Granger or Garcia, you will also need a backup SG as well. So, you have now spent 10-12 million to replace Hayward, when Hayward will cost you 14 this year. Is Granger/backup SG better at 12 then Hayward at 14? Nope.
If you go with Hood as your starting SF, you have essentially just fired Snyder and put yourself in the top 5 lottery again. You won't win with this lineup:
Burke
Burks
Hood/Jefferson/Marvin
Kanter
Favors
Who plays defense? Who passes the ball? Heck, who is your secondary ball handler? Letting Hayward walk for nothing sets you back three years as a franchise. Resigning Hayward MAY, might, maybe will hinder one year when it comes to salary cap scenarios. And no, I'm not worried about Burks or Kanter getting max deals, because they most likely won't, and if the do, I match the offer and have until February the next year to decide who to trade. No big deal.
Matching Hayward gives Snyder a good player to work with, keeps fans happy, keeps a guy you developed and lets you enjoy the fruits of your work, doesn't hurt you financially.
Letting Hayward walk doesn't help you at all. Is there even one positive for letting him walk? So you can tell your next employer, because you lose a ton of games the next two years, that you played hardball?