You shouldn't have to fear the mop buckets! I'm not knocking standard janitorial crews but there's a LOT more at stake and a lot more going on in a data center than than a janitorial company is equipped to deal with. We're talking about millions of dollars worth of equipment and data in a facility and no standard janitorial company I know of has insurance and liability for this.

That said, they aren't trained in the environment (other than what you tell them) and more than likely aren't going to be using equipment and chemical designed for a critical environment. They also won't be able to provide consulting and expertise relevant to your facility such as particle counts, environmental audits, etc. And do you really want untrained janitorial crews in your subfloor without the right equipment and experience?

As for the importance of regular cleanings and audits, the cost is a fraction of the potential downtime contaminants and related issues can cause. Quarterly or monthly cleans are the industry standard (regularity of the cleans is dependent on the traffic and speed of particulate breakdown in the critical environment) currently. The vast majority of data centers in the US employ specialized third-party companies to service their data center, cleanroom, or computer room. It's hard to put a price on a clear line of expert accountability and peace of mind.