It sounds like what you are describing is a "server", not a "streamer", which often includes a DAC. If you're expecting a server to vastly improve sound quality, you're correct in your assumption that it will have much less impact than the DAC will.
I went from a Roon Nucleus to a much more expensive server and was frankly somewhat disappointed that there wasn't much difference in sound quality, however there are good reasons to have a good server (which I consider the Nucleus to be) - onboard SSD storage, Roon compatibility, better connections to the DAC among them.
In my case, the server I have also includes a top notch CD player that reads the CD into a buffer on the streamer, upsamples it, and sends it to my DAC. It also has i2s connectivity and the two pieces are from the same manufacturer and designed to play well together. One of my previous DACs was not ROON ready, but connecting it to the server allowed ROON to "see" it.
My opinion / experience is that for most people an expensive server will have little if any impact on sound quality, but may offer other benefits.