So light bombers were mostly due to the expense of bombers- it was a cheap, economical way to have a bomber, and to have one capable of operating from less-than-adequate airfields. They WERE used quite a bit, but soon got their roles eclipsed by medium bombers like the Ju88, B-25, B-26, and such, which were capable of bigger bomb loads, more armour, more attack capability, and could operate from similar runways with more powerful engines and such. Basically, the light bomber was a stepping stone to the great medium bombers of the war.
As for heavy fighters, well, there is a LOT of myth about those. To summarize as best I can, most of the mythos comes around from the Me110 and its performance in the Battle of Britain. The myth goes that Me110s were a total failure, couldn't dogfight, and soon had to be escorted themselves by Me109s! Like any myth, there is a nugget of truth in it- the Me110 could not dogfight really. It could turn with Hurricanes easily, but its big problem was that, due to the wing span, it couldn't roll quickly, so a good Hurricane or Spitfire pilot would bank one way, get the Me110 following, then quickly bank the other way, something the Me110 pilot couldn't really do, thus getting him off the tail of the Spit/Hurri.
The big issue is that a lot of people apply that to heavy fighters and go 'see so they suck.' The problem is, these people seem to assume that there is only one method of aerial combat- that of the dogfight. What they're not looking at is that heavy fighters were NEVER, I repeat, NEVER supposed to be used that way. The training doctrine for all heavy fighter units was to be boom and zoom fighters- and this was where they excelled. Due to their wing size and two engines, the heavies had much better climb rates than single engine planes, and that plus their weight meant they also have very fast dives. The optimum way to use a heavy fighter was to fly high (and thanks to those wings/engines, they had higher ceiling levels than single engine fighters), and basically conduct fighter sweeps, booming and zooming any flights of planes beneath. In the main idea of the Me110, it was to fly high, dive on an enemy formation, use the concentrated fire in the nose to break up that formation (possibly taking some of it down), then zoom away and climb back up to escape. After that was done, a following unit of Me109s would come into the now broken, scattered enemy formation and pick it apart, while the Me110s went back to overwatch, diving on escaping enemy planes/breaking up anyone who came to rescue. This was the doctrine for the P38 as well, and somehow we don't see people claiming the P38 was an 'obsolete, useless, niche fighter'. Instead it's considered one of the best day-fighters of the war- and the big reason is that the US stuck to using those tactics for the majority of the war.
The Germans though, had a quandary during the battle of britain. The Me109s simply could not keep up with the bombers- they had about an hour's flight time, even with drop tanks, over Britian, and couldn't actually escort the bombers. The Me110 meanwhile could. Now, this might have worked, had the Me110s been flying high over the bombers. HOWEVER, German escort doctrine had the idea that escorts were supposed to fly at the same level as the bombers, maintaining the same speed (the idea being it meant faster reaction time to an enemy attack on the bombers). This, however, meant the Me110s were basically sitting ducks. They couldn't get up to speed, they couldn't dive, they were left basically unable to use their doctrines. The wings that were assigned to escort duty suffered tremendously as a result, while the wings that stayed in heavy fighter sweep mode did spectacularly well, leading to weird cases where one day, there might have been 10 or 20Me110s shot down, and then in the next day, another Me110 wing would take out 10, 20 RAF fighters without loss. The fun information is that, during the BOB, the Me110s actually scored the SAME kill to death ratio as the Spitfire, and outperformed the Me109, despite these losses. The big reason the Me110 disappears from the skies over England towards the end of the BOB though is production- the Germans only entered the campaign with less than 300 Me110s, lost a bit over 200, and simply were unable to keep up with the losses. The Me109 suffered just as badly, but having started with greater numbers and production, was able to keep in the skies. The Me110 had never been expected to take much in the way of losses due to the doctrine of not sticking around to actually do combat, and so when it was forced into that role, there was not the production or numbers to keep it up. It was supposed to be the tip of the sword, and that's all.
In the end, the myth persists because yes, heavy fighters were sitting ducks when tied to escort duty. As the USA experimented with escorts, the P38 was pressed into service, and basically did as well as the Me110. It was pulled out, later replaced with the P51, and went back to doing awesome work as a heavy fighter over the ETO and PTO until war's end. But all that does is validate the heavy fighter in its role- it was a boom and zoom sweeper, NOT a dogfighter. It was never meant to stay in contact with enemy fighters, and failed when pressed into that task due to the needs of the generals.
Hope that's an ok summary, lemme know if you have any more questions. I can try and find the actual KDR's of the 109, 110, and Spit/Hurri in the meantime.
Ah, here it is:
Spitfire 550 victories to 329 losses – a ratio of 1,7:1
Hurricane 750 victories to 603 losses – a ratio of 1,2:1
Bf 109 780 victories to 534 losses – a ratio of 1,5:1
Bf 110 340 victories to 196 losses – a ratio of 1,7:1
