From: Bratislava, Slovakia
Eventually most of the P-39s and P-40s were relegated to ground support roles as fighters with more range/altitude/speed went into combat and the air superiority was achieved.
Actually P-39s were used on Guadalcanal for ground strafing and bombing in 1942! Australian Kittyhawks took strafing at Milne Bay at that time too. New Zealand Kittyhawks and Corsairs serving in Solomons after the 5th/13th AF moved forward were relegated mostly to ground support sorties - as almost no enemy aircraft were around. Also most of the RAAF was in late 1944 occupied by "suppression" of enemy air activities as the combat moved to the Philippines - this included regular bombing and strafing by all available planes - Beaufighters, Kittyhawks, Spitfires - eventualy leading to so called "Morotai mutiny" - as the pilots thought they were not used properly.
In the ETO the first effective "Tactical Air Force" developed from the Desert Air Force - Hurricanes become Hurribombers, and Kitthawks turned to Kittybombers - strafing and bombing anything that moved. As more P-38s, P-47s and P-51s flowed in to take over air superiority role and bomber escort, the short legged planes were used over the battlefield or in the rear. Spitfires, A-36 (first P-51s with Alison engines), Hurricanes, Kittyhawks, P-39s, P-40s, even the P-47s were more and more used to attack ground targets.
You can actually notice this trend within the game too - first versions of fighters are gun only (P-40B/P-38E), later a 500lb bomb or two (P-40E), yet later model even carry a 500lb+2x250lb bombs (P-40N), or even 2x1000lb (P-38J/L/M), etc.
Are you flying a tactical escort mission for light/medium bombers to some nearby target? Oh, then you surely can hang up a couple of 500lbs under the wings, ney? Wanna flak suppression around some supply dump 20 miles behind the frontline? Just carry these two babies and loose them over there. Wanna isolate the battlefield? Well there is a bridge/tunnel over there... Why putting up a mission for a Medium/Heavy bomber group if a squadron of P-40s can lob the bombs over there?
"Dive bombing" was actually more like glide bombing - true Dive bombers needed dive flaps to slow them down (SBD Dauntless, Vengeance, A-36, A-24) and could dive up to 90deg angle. Regular planes without them eased on throttle, and put themselves in around 40-50deg glide - unless carrying a time-dealyed fuzes in which case, they would skimm the ground and skip the bombs all over the place.