That has a lot more to do with the dated implementation and less to do with digital radio. There are a number of digital broadcasting techniques which can minimize and compensate for noise, including a slight delay with a signal correction and fault tolerant codecs.
DAB was implemented using the old MPEG2 audio codec. DAB+ uses the now 15 year old codec HE-AAC which isn't really designed to handle corruption. Opus handles loss a lot better (see their examples https://opus-codec.org/examples/ )