Sometimes being offsite helps too
I was doing offsite work for an employer after I left the west coast for the east which worked out great that I wasn't there. They had a major customer that frequently called at the start of the business day EST. The company was small so that meant either the owner or the dev lead got calls 5:30 in the morning. With me being in the EST it just meant I was getting a call before I left the house for work. So having me do parttime dev work + cover the morning oncalls worked out for the stress of the company.
In short: a consultant can be a dumping ground for things that are painful for your employees to do but easier for them to do for some reason (access to hardware with a different flavor of OS that they prefer, timezone they live, proximity to customers you need input from etc).
