I actually think Rhaegar ‘looking’ like Viserys adds another layer to Viserys character. He would’ve remembered what Rhaegar looked like; how handsome and Royal he looked. Viserys would’ve looked up to Rhaegar, so it makes sense to me that he copied him, tried to emulate him.
“What did he say?” the man who had been her brother asked her, flinching. It had grown so silent in the hall that she could hear the bells in Khal Drogo’s hair, chiming softly with each step he took. His bloodriders followed him, like three copper shadows. Daenerys had gone cold all over. “He says you shall have a splendid golden crown that men shall tremble to behold.” Viserys smiled and lowered his sword. That was the saddest thing, the thing that tore at her afterward…the way he smiled. “That was all I wanted,” he said. “What was promised.”