The US took a step towards that with CASE Act that was recently passed, establishing what is basically a small claims court for copyright infringement. The big problem with the existing situation is attorneys fees can be over $50k for a relatively simple case, and the average case costs over $200k. With the new system the process is streamlined and there is no need to hire an attorney, and attorneys fees will not be awarded to the prevailing party, except in cases of bad faith. The total damages are also limited to $30k, and $15k in statutory damages per infringement, so if you prevail it is less likely to be appealed

Parts of the UK and several EU countries have a similar system with a small claims court for copyright cases under a certain limit with a limited discovery, where attorneys are not needed in addition to the regular courts.