Well, the concern was never whether the console is always connected or not, it is whether it is REQUIRED to be always connected to work (e.g. mainly play games).
If it's not implemented in a balanced way, it will become an unfair race where dudes who can afford (or are crazy enough) to spend real money will have a significant advantage. Then, it will obviously not be fun anymore.
Or worse, selling a machine so badly designed that there's a dedicated Wiki documenting the flawed console's technical problems: http://en.wikipedia.org/wiki/Xbox_360_technical_problems
dysonlu's comments