You are right the tourney factors multiply but have drawn completely the wrong conclusion. If you have high expansions and research then 1 AW level is a bigger numeric increase in the tourney squad size and thus a bigger numeric increase in troop losses. But because squads are also already larger the benefit of the sanctuary (reducing troop losses by at least 0.75% per kp level) is also larger in terms of number of troops.
Both factors work as percentage changes to your current troop losses per encounter, so we can simply compare the percentages.
Research and expansions have no effect on the calculation of sanctuary benefit since they increase both the cost and benefit equally.
The more existing AW levels you have the more beneficial the sanctuary is: at 0 AW adding a level adds around 0.3% to the tourney cost; at 700 or so existing levels it adds only 0.1%. The benefit remains 0.75% or 1.5% in either case. So the sanctuary is better the more other AW you already have.
Getting really far out there, the only thing that weakens the benefit of the sanctuary is if you can consistently add a lot of DA/UUU buildings. AFAIK the health bonuses add rather than multiply. So if you have 2 DA buildings for +100% health and a sanctuary giving +20%, that sanctuary is increasing your health from 200% of default to 220% of default: ie it's actually a 10% increase on the value-with-DA-but-without-sanctuary. If you can consistently add more than 100% of health boost (more than 2 DA, 4 UUU or mix) AND have few AW levels then the sanctuary benefit can become very small as these other health bonuses are diluting the sanctuary bonus. The only way to get more of these buildings consistently is to have a max timewarp and polar bear allowing 2 entire tournaments to be done in one building placement. So with a max timewarp, no other AWs at all, and throwing diamonds at the MA to respin to get more UUU you might just about reach a situation where sanctuary kp-upgrades didn't help. Or if you cater the tournament of course
But back in the real world all sanctuary upgrades are beneficial for all cities for fighting the tournament.