I have analyzed this information before, and this is what the chart looks like with one line for each weight category if you convert the temperature and pressure altitudes to density altitudes and then chart that vs. the takeoff distance:
You can see that I have drawn a sort of best-fit line for this information. I did not add humidity as a factor because the manufacturer's charts had no relevant data.
Clearly, the trend from the manufacturer's data, when converted to density altitude, does not appear perfectly linear if you follow the data points they jump up and then start lower again in chunks of similar density altitude.
The greatest variation here is about 400 feet from the highest point in any of those clusters to the lowest point in the same cluster. That would be the yellow line around 8,000 ft of density altitude.
To answer your question, maybe they didn't use density altitude in the POH because their data appears to be irregular.
With that small margin of error here, I am comfortable using these best-fit lines to quickly calculate my data because I wouldn't make a go descision for a takeoff with a calculated distance anywhere near being within 400 feet of acceptable runway length.