Partial Boil cold break

Question,

Is there any reason I shouldn’t do a partial boil then bring it up to the correct level with chilled water at the chilling stage? I’m thinking if I start with 5 gallons, by the time i’m done with the boil I should easily be a gallon short of my 5 gallons. Once the temp of my 4is gallons of wort hits about 100 degrees, I could add water chilled from my refrigerator to get it to temp quicker. Is there any reason this is a bad idea?

When I was doing partial volume extract brews, and before getting an immersion chiller, I used to top-off with ice.