Mark 3s will never be the new mark 1s. The majority of preserved steam locos are either BR era or pre-nationalisation designs that operated under BR and hauled mark 1s in regular service, so look fairly authentic hauling them. They would look incongruous hauling mark 3s.
The same goes for many of the core fleet of preserved diesels around the country, which often carry sixties or seventies liveries, were withdrawn in the eighties and will never or rarely have worked with mark 3s.
Mark 3s also do not have vacuum brakes and cannot be steam heated. I'm unsure if all preserved steam locos are fitted with air brakes. Also, while mark 1s are notorious for suffering from corrosion, they are fairly basic vehicles to maintain within the sometimes limited capabilities and facilities available at many preserved railways, while mark 3s are electrically more complex and, I'm led to believe that, being air conditioned, suffer from damp quite badly if left standing without a power supply or out in the open for an extended period of time.
While 'Tornado' will have a rake of mark 3s prepared for it for railtour duties, that is something of a special case and I'd argue that introducing mark 3s to the majority of established preserved lines would be to seriously undermine the ambience of the inter-war or 1950s "chocolate box" atmosphere that many strive to achieve and maintain and is the key selling point of heritage railways.