There are a couple of things that you seem to be confusing hereof not fully understand why Bitcoin is valuable. Any technology that reduces friction will be used by criminals and there is nothing you can do against it. Whenever something is useful for people, it will also be useful for those with bad intentions.
The good thing about Bitcoin is that the authority has an advantage on tracing these criminals. Due to the blockchain transaction being transparent, authority can use enhanced tool in tracking illegal activities. Just as the earlier reply stated, there is more chance of tracking illegal activities in Bitcoin than the traditional fiat.
I also doubt that it would have any influence on the overall amount of crime that is being committed. They have found ways ever since to commit crimes even before Bitcoin existed. How would you even go about it? If you change the codebase for Bitcoin, another crypto will pop up. Think about Monero. Whenever there is demand for something, someone will build it.
In essence you are intending to turn Bitcoin into something that people don't want. Imagine how many technologies can be used for evil and we still use them.
As far as I understand, Bitcoin had its own anti-fraud system, it is also one of the reason why blockchain transactions is available to the public. If only authority can take advantage of this opportunity and learn how to use it in tracing illegal activities, Bitcoin natural feature will greatly reduce AML and other illegal activities that appears in the Bitcoin ecosystem.
That definitely depends on the person using the network. All too often those people who want to stay anonymous for whatever reason either make mistakes or don't know how to exactly go about it. It also depends on what kind of crime it is all about. I guess if someone pays for weed then law enforcement is probably not even interested in the person buying it.
I think authorities are on top of their game by now and it is not as easy to use Bitcoin for legal stuff as OP suggested. Most probably freaks who are into child abuse and what not are likely using Monero anyway. That is what I mean. Let's assume Monero would one day be cracked, well, there is still demand for an anonymous currency and someone would try to build it.
When forum members talk about the $5 wrench attack when it comes to crypto, sure that can happen anytime. But that can also happen when people know that you are storing gold bars in your basement or expensive art. In the end all these criminals usually look for an off-ramp and that is where it becomes difficult I think.