OP, You obviously have never performed any of these feats...Or I assume you have nor from the stance of your claim and the validity of the same claim.
As someone who has worked in the most dangerous of industries (Commercial fishing in the Bering), and also has worked with both very strong and very agile individuals, I refute that Strength=Agile, on the grounds that no amount of strength will help you to dodge unlashed gear on a rocking boat, nor is the reverse true, your agility will not make one iota of difference when you go in the drink to heft yourself into a life-raft. Furthermore I have done my fare share of rock-climbing, traversing negative slope requires strength, making a leap to a handhold ( brave/foolish) is a feat of agility...holding on requires strength....
They are not one and the same.
And yes, you could combine them into a single roll....for instance an Athletics Check(5E) and use the correlating Ability Score as needs be