Tough one all around for me. I've been giving this a fair amount of thought recently and I'm pretty sure I'd hate it but I could learn to live with it.
The plus points - for a team that's pretty cash-strapped if they keep Tyrod, $6.8m is a lot of money to free up. If this is a rebuild, a 34 year old dude on his last legs probably isn't going to be the difference maker in the long term. It would give the team the best chance at getting some value out of Adolphus Washington. He also has a $500k roster bonus due in mid-March, decision has to be taken quickly (akin to ripping off the plaster nice and early, let people accept it).
The down sides - Kyle is the heart and soul of the team, his veteran leadership could be vital in the early stages of what it seems Sean McDermott wants to instill in his charges. He's still a capable player in his twilight years. We don't really have anyone capable of replacing him as a full-time starter just yet so we would need to acquire one early in the draft or a mid-tier FA to at least rotate with Washington.
I see the logic if they do it but, if you follow me on Twitter, I'm going to apologise in advance for my language on the day that happens.