What? Don't grind your case for that!
If a 13-tooth sprocket doesn't fit - return it (or sell it), and work out something different.
What gear combination are you trying to achieve that isn't possible with a 9, 10, 11, or 12-tooth front sprocket?
Are people having trouble finding rear sprockets, or something? There are kids quad ones that fit...
If a 13-tooth does not fit without grinding, the tuner's spreadsheet should be updated to say as much.
Could someone confirm that this is definitely the case for all Minarelli cases?
Okay, there is one reason to go big - the more teeth on the front sprocket, the better it engages the chain.
This will reduce wear over time. Slightly. I don't think you had a huge chain-wear problem with your 9-tooth, so a 12-tooth will be an improvement.
It will be even more of an improvement if your rear sprocket has an even number of teeth, but I really don't think that chain life is why you're re-gearing...