A bad team is exactly the team someone like Meyers should sign with, you'll get PT right away, and a chance to establish yourself as you go into your RFA years - instead of spending 2-3 years bouncing between the AHL and NHL and on the 4th line.
It's one thing for a player like Fox to threaten to go FA and pick his spot, he knew he'd be top 4 where ever he went.
Someone like Brink has upside, but isn't a sure thing, and could be buried on a deep team where there's no spot open on PP1 and they're not sure what role they'd like him to play - meanwhile with Atkinson out, Brink will play 15 minutes a night here and be penciled in the top 9, if no the top 6, and PP1 next year. So he could establish himself a year or two earlier than if he went to a deep playoff team.