“How much do you have to spend on a DAC to perform better than many turntables.” Let me try and address that. Obviously it depends.
But the best way to look at it as your digital end versus analog end.
Digital end: Streamer (or Player), and DAC
Analog end: TT, cartridge, and phonostage
Twenty years ago digital could not touch analog at any price. But slowly digital has improved and the price differential has been dropping. At this point, for carefully chosen and synergistic components there is perhaps a small advantage to analog… say 10%. There is nothing exact about this… it is so highly dependent on every piece of equipment you own and the performance level of your system.
My system performs in, say the highest 10% of high end systems. My analog end cost around $35K and my digital $40K. The sound quality is equal. When the analog vs digital end get down to $5K… I’m not really sure what happens… but I suspect the analogue lead jumps ahead. So, you need to put a lot into the DAC and streamer. At this level, you’ll probably have to invest In $8K + to match the analog.
Obviously this is constantly changing as folks innovate and better sounding components and techniques become available to manufacturers. For instance the Schiit Yggdrasil is only ~$2.5K and performs like a number of DACs over $5K. But make no mistake about it… if the rest of your signal path is capable of resolving it… the $10K DAC will blow it away.
If you are interested in high end sound quality and choose good quality and synergistic components… you get what you pay for.