The probe in simple installations should be on the hottest cylinder...and yes it would give you 'most of the required info'.
However it doesn't give all the info...and the hottest cylinder can change due to local airflow effects in different phases of flight...not to mention over time as other things impacting cooling change...like baffles wear out etc.
Instruments like the EDM 700 and their competitors really should be considered essential by aircraft owners...I am at a loss to understand why there is such resistance to installing them...they are not THAT expensive and pay for themselves in a VERY short time frame just on fuel saved let alone engine wear etc.
When I last flew my mate's C180 in the UK late last year (the first time I had flown that one since the late 80s) I was surprised to see them not leaning at all. The reasoning was that it was a waste of time etc on the reletively short low level flights they typically did. I explained some of the issues and for the flights we did on that day I leaned appropriately at all times...including after start and taxiing etc.
We flew three sectors from their farm strip north of WW to IOW, back to WW for fuel and back to their farm strip....never above 2000'. Leaning the mixture gave smoother running and saved almost 20 liters/hr that day over what they considered normal...at GBP1.40/liter!!!! Do the math...it was a HUGE % of what they charge themselves to fly the aircraft.
Twas a wonderfull day...been a long while since I'd flown a Cessna taildragger, let alone that one...I think I'd last flown a C180 in the late 90s...can still do a nice 3 pointer on grass
Shock cooling is a bit of a myth as well.