The question is : If all classes have or need a way to bypass, ignore, change damage type, why bother with monster's resistance and simply don't have them.
Because it's not that simple by a long shot.
I may be able to bypass your resistance, but it's going to cost me an action that I could have spent doing something else.
I may be able to change my damage type, but I don't have as many effects/feats/items that key off this damage type, so I am less effective.
I may be able to ignore some of your resistance... but it's only some.
Either way, I am now less effective. But, since I'm a specialist and yet I do have some means of countering your resistance, I'm not useless.
And on the other side, permanent resistance, especially Necrotic, poison and fire, makes the game too easy for players.
Hardly, as in 4e monsters had the same means to bypass, ignore, or change damage types that players had.
Most of the time for monster "Vulnerable = Rapid death and no challenge". If every time I put undead vulnerable radiant I must adjust upward the xp budget there is a bug.
Somewhat true. The best way to handle vulnerability that I've found is not with increased damage, but with turning off an aura, gaining combat advantage, losing insubstantial, etc., etc.
Why keep it? Because at some level, rock-paper-scissors is fun, and it's also good to see proper planning pay off.