Yeah that's a great idea. Im sure it wont over burden police depts and keep them from investigating actual rape cases and locking up the perpetrators.
People having sex could conversely could just do it responsibly. If a woman is using birth control the man is using a condom and they don't have sex during the 6 days she's actual able to get pregnant the chances of having an unplanned pregnancy drop to essentially zero. I know is nutso to expect anyone to exercise any amount of self control and responsibility these days, but...
The pill is 99.7% effective if used properly.
Condoms are 98% effective if used properly.
Add in the timing aspect and if you get pregnant it would border on being a miracle.