If you get an insert of appropriate size/cfm you shouldn't have any problem with grease. You have to clean the baffles and the liner on occasion, but the outside doesn't get dirty at all.

I have a 36" range with a white painted hood over...I've not had any grease problems.

If the hood is 6" wider than the cooking surface and at least 24" deep, you shouldn't have any grease issues.

I've had my 42"W x 24"D hood over a 36" cooktop for over 7 years and all I have to do is clean the squirrel cage occasionally and wipe dust off the outside of it....no grease or gunk!

I have a small (by GW standards) under-cabinet hood, stainless. But it vents directly outside, and we use it all the time. It doesn't get greasy at all - and we are serious carnivores.

There is a reason restaurants have all stainless hoods. There is a reason architects specify solid surface for surgical rooms in hospitals.

I have a stainless 36" hood over a 30" range. We always cook dinner at home...I mean every single night, from scratch, messy cooking. I have had the hood in use for well over a year now and have never had grease on the outside...dust, yes...grease, no. I wonder if maybe your hood is too far from the cooking surface or not enough cfm's.