That's a very serious allegation. It should be investigated in any case because:
1. Dr. Ford deserves the right to have her claims verified, just like any other potential victim
2. If Kavanaugh is not guilty, he deserves to serve his life-long term without the potential black spot on his image; otherwise this will be always attached to him, for life
3. If Kavanaugh is guilty, well it's obvious, he must be asked very politely to f$$k off

The only scenario in which an investigation is not welcome is in case his supporters have a doubt on his credibility and he himself is "oh, shit, I was so pissed did i really do that?!"