In an ideal world where everyone was a rational, disinterested superhuman who devoted themselves to a scientific pursuit of truth, only ever focusing on arguments would be the perfect approach.
Unfortunately there do exist people who deliberately and knowingly bullshit other people in order to get what they want. Such people absolutely win from a policy of "attack the argument, not the person" because their goal is not to further understanding or even win arguments, it's to confuse people into acting a certain way ... often paralysing them into inaction by creating the appearance of an unending debate.
Thus refuting one bullshit argument simply results in two more popping up to replace it. Even if some people remember the first argument that was refuted, this doesn't help, because:
• Lots of other people won't remember the names of who was involved, or won't be aware of the previous arguments at all.
• Of the people who do remember, the fact that a debate was happening at all may be taken as evidence that the people involved must be "experts", and thus the fact that they lost the argument doesn't necessarily reduce their credibility.
• If someone was a good enough bullshitter to require a response in the first place, they will probably be good enough at it a second time to ensure that if they get no response, some people will start to assume they must be correct.
This can rapidly turn into complete defeat by the people who are actually making reasonable points because they simply become exhausted and burn out faced with an unending wall of plausible sounding nonsense, which then eventually replaces reality with itself.
I've seen this problem play out in brutally sharp detail not so long ago. The people involved knew they were bullshitting, but didn't care because in their eyes it was all for the greater good.
The only solution to this is, in fact, to attack the credibility of the people doing it once they have repeatedly made absurd or invalid arguments, because otherwise it's much harder for people to learn to tune them out.