The article that I posted kind of concluded "Thus, under identical load and on the same dry surface, the wider tire has a greater contact area and develops higher traction, resulting in greater stopping ability.", which is speaking to something different than contact patch varying with load.
The contact patch often doesn't vary that much with load, which is why tire size matters a lot once one is hitting some limits of traction. Note that depending upon the conditions one meay want wider tires for better traction in dry conditions or when one needs to 'float' on surfaces like sand, mud, etc. or narrower tires for higher load per contact patch such as for water covered surfaces or on winter tires.
The contact patch often doesn't vary that much with load, which is why tire size matters a lot once one is hitting some limits of traction. Note that depending upon the conditions one meay want wider tires for better traction in dry conditions or when one needs to 'float' on surfaces like sand, mud, etc. or narrower tires for higher load per contact patch such as for water covered surfaces or on winter tires.