It would create a burden on businesses to keep all records indefinitely (most businesses only keep around 7 years of most records). This has a monetary cost to it that would disadvantage mature businesses against younger ones.

It's not just a burden for the immediate parties. Having the ability to dispute rights and obligation going back indeterminate amounts of time adds risk to the rights and obligations of untold numbers of third-parties; everybody's interests become more interdependent and intertwined the more time has elapsed. One of the important functions of a legal system is to settle rights and obligations. Settled, transparent rights and obligations are also integral to notions of fairness and justice, so it's not a zero sum thing that statutes of limitations sacrifice fairness for cold transactional efficiency.

In an era of digital records keeping, this does not sound impossible.