You're more or less correct, but a lot of onboard audio is poorly isolated which results in notable problems.
That said, I would rate the importance in an audio chain as follows:
Source of audio (mastering matters a lot, as does file quality) > AMP/Speakers/Headphones > appreciable cables, a cheap sufficient gauge copper wire will almost always be indistinguishable to higher end options and you do not need to spend silly money.
DAC fits in weirdly but should if decent be the last part of the chain, a £50-100 DAC with the right bit rate will be absolutely fine. People tend to conflate DAC with "device" which includes a ton of features, rather than the actual chip doing the work.
I used to do headphone and speaker meets, met many a person that spent bucketloads on DAC and wire but either flat out refused to do double blind tests or when they did failed horribly. Usually older gents with more cash to spend that refused to acknowledge that hearing diminishes with age much like everything else, but the same absolutely held true for the handful of younger people involved.