I imagine it's because it would kind of defeat the whole purpose of Dalinar shifting his goal. He's set himself to turning The Blackthorn into a politician, and is actively distancing himself from the days of battle. Shardplate, as awesome as it is, is a tool of war meant for combat. It has deep connections in form, function, and cultural consciousness, and Dalinar wearing Plate would immediately make everyone think of him as a warrior, even those who have never even heard of him before. It's also not really practical for day to day things. Theoretically, he could wear plate while acting as a general in the field, but that means there's one less Shardbearer fighting on the front lines or ready to be deployed to where he is needed most, which is not what is needed.
So the only time in the future he'd be wearing Shardplate is if it was lent to him by a Shardbearer under specific circumstances. So there's no point in him having it.