Agree that a good preamp will do wonders. While the DAC may have a decent volume control and analog stage, it likely cannot parallel the sonics of a quality, dedicated preamp. Most DAC volume controls are digital in nature and their analog gain stages are an afterthought and do not deliver optimal gain and harmonics, all while offering a low noise floor. One of these three are typically sacrificed.
The only DACs with built in preamp I have ever loved are the T+A SDV 3109 HV (but hey, that’s $38,900) and the T+A DAC 200, which has a quality equivalent of a $3K preamp built into it. I’m sure if you get into DACs $15K+, then their volume control / preamp sections will be better.
Oh, and I did own the PS Audio DirectStream DAC MKI - heavily modified with upgraded Edcor transformers, Farad Super3 linear power supply, etc. Owned it for many years, and I always always always preferred it with a separate preamp.