I watched a video about using a power conditioner to supply AC current to your physiccal audio rack units. It made me cry 
in the first part when he demonstrated how much noise can be on a power line.
Does anyone have a power conditioner in their studio? Is it necessary? Would it stop any hiss and hum on mixers and units (such as dbx 286s)?
Looking forward to hearing some thoughts!
Define any problem first and then deal with it.
A professional UPS will have smoothing circuitry.
Keep all mains cables away or shielded from cheap audio leads.
Use Ferrite blocks to help reduce RF.
In the old days, we used to physically remove the pesky little power supplies from the rack units to a remote power rack to kill rattle and hum.
Love the Ferrite tip @The_Tone_Arranger!
Now a pro UPS is going on my studio list but it should be very quiet 
Calculate your amperes/current load requirement, add 20% then go for a 5 minute deferred shutdown time limit.
It doesn’t go in your audio rack for obvious reasons. It goes in your remote power rack or better still, a dedicated machine room. Also consider (seeing as you’re building a clean install) putting in a clean feed mains supply in directly from the consumer unit with nothing else on it. As domestic appliances get on in age, Stats in Freezers, Fridges, Immersion Heaters, Washing Machines, Tumble Dryers, Dishwashers and timer switches can make a noisey spark/arc as the contacts get dirty and worn over time. Mains spikes is another consideration that in some cases can cause permanent damage to sensitive computer power supplies.
The only audio component in your setup to earth directly to the mains, is the Soundcraft mixer. Lift all other earth plug top connections. They will find their ground through the mixer and eliminate earth hums and loops.