great question jonboy. I think changing different indicies, futures etc. to match the market their own market hours would make things faily complicated. But that said it would be up to the trader. It may make things more simple for you. I used to trade futures and it seemed almost everything had different hours (even though they trade after hours on globex). Wheat would shut down trading in the morning for me for about 45 minutes or so while ICE had different hours.
I left my charts times alone, but had the different market hours posted above my computer so I could see them at a glance. I'm not sure if I answered your question. Basically, it's up to you and what makes thing the easiest.
i think it make sense, especially when doing daily bars analysis. (to change indices to reflect the trading session of that country) and you can see the gap up/down, if its 24 hour charts, its like 24 hour price movement, futures and normal session blended into one...
if youre actively watching and trading the market when it is open, then it doesnt really matter for intraday, as thats happening now, the start time is not an issue on charts as youre living in the moment, as youre viewing the price in real time.... but when longer term analysis on dailys and end of day, then it can be an issue, i think. Im not 100% sure, just thinking aloud here...
eg FTSE is 8am to 4.30pm uk session, my chart was showing 24 hours of ftse pricing, but after changing it to show only data for that time period... it makes sense i think.
I wonder how professional traders set their charts up.
cheers.