It depends what you mean by regulation.  Most likely you mean the modern government variety.  So as related to an exchange it would mean some set of rules some bureaucrats devise to attempt to solve past problems.  What do you think the chance the bureaucrat will consider tools so customers can personally validate their holdings or mechanisms for multiple parties to check each other in real time.  All technically possible.  Or better yet distributed exchanges.  Instead they will use the limited technology they know and government force to impose a less efficient and effective set of rules that can't be easily avoided by those who develop better methods.  It will also create the pretense the problem has been solved reducing the motivation and profit for providing superior solutions.  It might seem to help in the short term but the long term results will be a system in the general sense in less well regulated.

It also creates an incentive for regulatory capture where powerful parties supposedly regulated by government have an incentive to collude with the regulators to have regulations or laws changed to favor them over less powerful competition or even new entrants.  This essential gives private organization indirect access to government force.