Granted, the GM just ruling things differently or filling out certain gaps is always an option, in every system

But in this case, i donīt feel that the RAW is intended to be that "malleable". If there was a single line that would support to use Strength instead of Agility, that would have already been brought up in discussions about the matter. Itīs a good idea, but only for those who like to stray from the sacred texts (or for the combat supp?)...
Although I already do have a preferred houserule in place: What about allowing Melee Attackers to completely switch out the role of Agility and Strength? Like, you roll with Strength + Unarmed Combat and add Agility to the Base Weapon AR (or Reaction) instead? That makes Strength more valuable
and adds a bit of tactical variety. That could be employed as an additional Combat rule or via a cheap "Martial Arts"-Perk.
Apart from Melee: Itīs generally weird how few checks actually use strength, even without looking at Melee Combat. Running and pretty much all Athletik tests is linked to Agility now. RAW, not even
Lift and Carry uses Strength in the actual dice roll. Itīs only related to strength because the hits add to the effective Strength for the Lift/Carry calculation.
A calculation that is
totally messed up right now, because once again, someone didnīt understand how exponential growth works

So, thereīs your 100% RAW-supported answer on why to put points in Strength: So you can bench-press a car.