Luxury is a matter of perception. If you can’t even afford taking a bus a guy on a bicycle has a luxury. If all you have is a bicycle someone with a used car has a luxury. Someone with a used car sees someone with a new car as having a luxury.
Today’s cars are equipped with all manner of things that at one time were considered luxury options including things taken for granted like automatic transmission, power steering, power brakes, a right hand mirror, tinted glass, rear defroster and so on.
We can assume if TOS had had more time and money they would have dressed their sets more, but we still have a 1960’s perception of what luxury would be for service personnel. TMP shows us a refit of the ship, but it doesn’t really look that much more luxurious than the TOS E, but looks more detailed.
It’s in TNG we see absurdly spacious areas for a service ship meant for the rigours of space exploration. But in TNG’s defence the original concept for the 1701D was that it would be “out there” for 10-20 years. Thats also why families were allowed aboard. But as the series played out that concept evaporated. As such a ship like the TOS or TMP E, or Picard’s Stargazer, could easily have done what the 1701D did.