Needed is a strong word.
The 30mm was specifically developed because a bomber could take quite a lot of 20mm hits, as only fuel tanks were vulnerable enough to reliably bring it down, while other hits were at most inconvenient.
The 20mm never was specifically an anti-bomber armament.
This is particularly apparent with the development of 20mm Mineshells, which were described as not destructive enough to bring down a large bomber structurally, but would make it more likely to destroy a fighter, simply from structural damage, making the entire plane a target and not just specific components.
In that sense the 20mm always an effective anti fighter armament that also worked well enough against bombers but 30-37mm cannons were really the anti-bomber armament.
As for the amount of 20mm cannons,
while one could bring down a plane with success, the general rule is simply more guns equals better chance.
The US development showed that you want at least 3000 RPM in 20mm cannons, better 6000.
Especially since with faster aircraft firing windows decreased.
The USSR chose 23+37mm canons to intercept bombers while the US went with high velocity 20mm cannons for air superiority fights.
Most WW2 20mm cannon armed fighters would have two, while twin engined heavy fighter and night fighters would generally have four or even more firepower. Only few would merely have a single 20mm.
A Dora with 13mm and 20mm armament was most suited to engage fighters while one with a 30mm was much better equipped to engage bombers as well.
And considering how a P-47 could easily take several 20mm hits, the 30mm also wasn’t a bad idea against certain heavy fighters.




