Are you really trying to assert that by not going after doz for having a vaguely close name in the same industry you would no longer be able to protect yourself from egregious misuse of your mark?
By not canceling doz's trademark you would be prevented from going after a hypothetical Mozz, who attempts to pass themselves off as moz by using similar branding and product offerings?
You and I, and your lawyer, all know that is complete fantasy. Yes, not going after doz may prevent you from going after similar companies who aren't really infringing your mark anyways... but you would still be fully able to litigate against companies trying to confuse your customers.
By not canceling doz's trademark you would be prevented from going after a hypothetical Mozz, who attempts to pass themselves off as moz by using similar branding and product offerings?
You and I, and your lawyer, all know that is complete fantasy. Yes, not going after doz may prevent you from going after similar companies who aren't really infringing your mark anyways... but you would still be fully able to litigate against companies trying to confuse your customers.