@chriss I started working on my corexy printer before they became popular. At the time I saw some forum posts from people who had built them using linear guides complaining that when the temperature in their shop changed 10 or 20 degrees, the XY mechanism would bind. The loose coupling for the X axis (and no additional support) was my response to that problem. I heat that printer to 50C when printing ABS and it never binds.
I haven't had any problems with first layer adhesion, either, even though the printer has no auto tramming or bed unflatness compensation.