That must be the problem. I don't own cheap clock-radios.

A clock radio doesn't strike me as an item one would spend
a lot of money on.

There have been some nice ones, especially from GE in the late 70s and early
80s. GE produced the first clock-radio with an electronic display (1972),
and the first with digital electronic tuning (1980). They were not cheap. I
have both.