I suspect the real reasons for the exemption are that it has increasingly difficult to apply modern standards to ageing vehicles. To perform an MoT on vehicles beyond a certain age means the MoT software needs multiple, and increasing, means of accommodating the many checks that cannot be performed. It also means that the person performing the test has to understand systems that no longer exist on current vehicles. As far as a voluntary MoT on an exempt vehicle is concerned I'm not certain that an"official" MoT can be performed - a safety check along the lines of an MoT can be undertaken by a trained MoT tester but cars beyond a certain age would all fail once the connection to the MoT database is established if only because of emissions checks.