English has multiple levels of formality. Colloquial English is several levels down from the most formal, academic writing and is also beneath what I call “good writing,” i.e. the standard English used in newspapers, magazines, books, and their online equivalents. Almost all spontaneous speech is colloquial, when not using even lower forms filled with slang and solecisms.
If politicians or others are using the expression good-paying jobs in colloquial settings, it is perfectly okay. I’d go further, and say that “good-paying jobs” is standard for most descriptions. Anything else would sound funny.