This thread is getting sidetracked a bit but thought I'd put my 2 cents worth in.
The reliance on measurements is as old as this hobby. Back in the 1960's Julian Hirsch was editor of THE major Hifi magazine at the time, Stereo Review and he was one of the first to promote the concept that measurements are most everything. He was an electrical engineer and that's what they do, they measure things.
Anyone who has been in the hobby a long time has experienced gear that measured well but didn't sound great. "Everything that can be measured can be heard but not everything that can be heard can be measured".
Now back to the OPs post. Different DACs have different output stages and implementations and will mate with different amps for better or worse. In one system I have a DAC that sounds very good direct into the power amp but to my ears sounds improved with a preamp, yet in my second system the same DAC not drive the power amps nearly as well and a preamp was definitely needed. A modern well made preamp will be transparent to the source but can add weight, drive and dynamics to a system.
I assume you have no preamp, just a power amp... and your system sounds good to you, then likely you can get by without a preamp, assuming the new DAC has similar output voltage. The gains you hear with a better DAC should be easy to hear. Then if you wants, buy a decent preamp on the used market and see for yourself, in your own environment, if its' a benefit. It's the only way you will know. If you find it adds nothing, you can easily sell it for what you paid. If you are building a new system, then getting an integrated amp does make sense as was previously posted.