Rolling radius change particularly if the car is lowered and also if the wheels are running a different effective offset to OEM (i.e. both lead to more risk of fouling under full lock or under compression).
Sidewall depth vs suspension stiffness vs UK potholes. 40-profiles are usually OK in the UK (going by mainstream cars with 225 / 235 / etc. width and typical modern saloon/hot hatch suspension...which is altogether probably pretty similar to us), but 35 and esp. 30-profiles seem to cause issues with punctures or (worse) bent rims.
Visual appearance if you combine both lowering (reduces physical and thus visual 'space' in the wheelarch) and bigger size (ditto, but visual only). Plenty of Yanks have gone to 18"s though, so have a hunt on Prime for some images / ideas.
"No man with a good car needs to be justified"
Blue '08 FD2 CTR - big, ITR-sized shoes to fill...
Yellow '96 NSX 3.0 - oh was it worth the wait!
Black '99 ITR - well, I had to have another one, the first was so much fun. Miss this one even more than #1...
Blue '03 S2000 - SOLD, flawed but fun
Blue '04 Focus TDCi Sport - SOLD, very good fun for a diesel!
Black '00 ITR - SOLD, still missed
Red '98 Civic VTi - SOLD, probably still bombproof