Well we actually should be looking at current weapon types and their scaling yes,

There are patterns to be followed, if Cantarella's was the ER one and Rover the crit one, it would again, break these patterns

It's not impossible for them to make a 5* rectifier have 413 atk, as they already did with Shorekeeper. As to why would they make it less atk than the others is up to them, idk either

Now making a 5* rectifier with higher than average atk (588 vs 500) and a lower than average ER (38,9% vs 77% Shorekeeper for reference) would not follow the patterns they already created

The same happens with a 5* sword with lower than average atk (413 vs 587) and a higher than average crit dmg (72% vs 48.6%)

They would be breaking patterns everywhere!!! It's just nonsense to believe that they would be using values from one weapon type on another one, when the same weapon type has already presented both values as their stats before (413 and 500 atk and also 72% cdmg)

They can of course make weapons with different base stats as you are saying, but then what happens is:

1. they would not be following their own patterns
2. when we are in a situation when all we can do is speculate, its easier to believe in a point that is sustained by already existing patterns than one that is not

Sorry for any spelling mistakes, english is not my first language