On the other hand, the people you get from the consulting firm, who were not hired with your particular needs in mind, and who are assigned by leaders who are both unfamiliar with what you do and have motivations which may not be perfectly aligned with yours, are normal people drawn essentially at random from a normal distribution. Maybe you don't need to have a particular skillset in house full time, but the person whose job is to do something will always outperform the person whose job is to maximize billable hours.
Then you sure as fuck don't want Deloitte within miles of it.
Personally consultants are just another tool in the mid-hi management toolbox. Just as a workforce on a payroll, this can be used in a good clever way and this can spiral into a shit show real quick.