I think people keep ignoring what a couple of posters have said, POH take-off charts typically provide pressure altitudes and temps however there is nothing to stop the pilot working out an equivalent density altitude and using that instead. It is just a convenience to help calculate, not a performance limitation.
If you had a density altitude that exceeded the values covered by the TO chart/table then maybe rethinking the take-off would actually be sensible. The only manual I have to hand at the moment has TO figures for a PA up to 8000' and temps up to 38C
This would mean you have a chart that covers density altitudes to over 12,000' (!)
eg
50C at Oodnadatta would have a DA I think a bit over 4000'
If you had 50C OATat Oodnadatta, although it isn't listed in the table, you pick the 4000' DA point (4000' and 7C) and you can calculate the TO distance just fine using that value. You are well within the calculated performance values even if 50C is not listed.
I seriously doubt there would be many times in Oz where a strip would ever exceed a 12,000' DA - and if there was - rethinking a takeoff in those conditions would make serious sense.
PPLs are required to understand and calculate density altitude as part of their theory course.