1. Me-262 was envisoned as a multi-role aircraft from the very start, inspired by the Mossie. Carrying bombs was not a problem.
2. Lack of nickel for alloys for engines ensured that they could never build enough to do any real good in any role.
3. Given item 2 above Hitler was correct in insisting that the few Me-262 available by 6 Jun 44 should be used as fast bombers to try to disrupt the Allied invasion since the Luftwaffe certainly was not going to do that with the other aircraft they had.
The "Fools used them as bombers" myth came from Galland, who was enraged at Me-262 being flown by bomber pilots (Luftwaffe had no bombers to speak of by that time) rather than his fighter pilots.
By the way the USAAF alone had 175 verified kills of Me-262.