No, I don't see any need for it.
Showing time zone in profile
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Well quite often I accept open seeks only to find player makes one move only and logs off to go to bed or work or some other reason for which they should really have withdrawn the SEEK !
it also helps to avoid bloomers like"Morning Kiwi" when its bed time !
Except for USA, I find the flags are sufficient. Australia's timezones have a 2-hour range, but 90% of us share one of the 3 timezones so it's near enough. I usually ask US opponents for their timezone so I'd be happy to have US players show Mountain Time or whatever in some way. I have noticed that not everyone can get their heads around timezones anyway, they can't distinguish between 5 hours ahead and 5 hours behind so the "Morning Kiwi" problem is probably insoluble. 
Also your post states made at 0835 am when u & I both know Kiwi time is PM !
I think it's a good idea. If possible, a small clock showing their local time/or time zone next to their name/country would be handy. If the member gives a specific city, even better. Surely it could be done. If a member merely says 'USA' then eastern time and western times could both be shown.
Would it not be a convenience to show the time zone in player profile? No world clock etc can give time zone for player who gives address as USA for example, which is commonly done.Occasionally someone states address is "International" etc. etc. It would be useful when looking for a quick response type of game challenge and the information is already requested by site in application procedures for timing purposes so could be readily available.(Currently I make a point of noting an up to date time zone in my location box for this and for social conversation reasons)