In general, I would have to say yes high quality DACs are converging on a similar good sound. About 20 years ago this was occurring rapidly between tube and solid state gear (particularly preamps and phonostages) where the issues with both were getting mitigated and the sounds converged.
I had a Berkeley Alpha Reference DAC along with my Audio Research Reference CD9SE DAC/CD player. I was able to route the digital signals through both at the same time and compare them directly with volumes matched by my preamp. These two DACs were so incredibly similar it was amazing… for High Rez files and CD or streamed content. Amazingly similar. After comprehensive comparisons I liked the Audio Research I tiny bit better… it had a slightly more fleshed out mid range. But very seriously good.
I also spent time with a top of the Line Linn DAC. Also, outstanding.
One thing to note is the sound coming from my digital end that it is very much at the same level and character as my really good analog end. That does not mean that every high end system will sound the same since differences in the amp, speakers, and preamp will have a different character depending on the musical objective of the company who makes them. All of my equipment is Audio Research… so, swapping just the DAC is a good test of this component. Had I swapped amps (say to Pass) there would have been a huge difference…