I have a thought on this that is not even fleshed through enough for me to make it an opinion.
The two rotation arms we have that depend the most on throwing a variety of pitches well in any given stint IMO are Porcello and ERod. While they all throw a variety of pitches, in most instances Porcello and Erod are the most unsure what is going to work for them in any given stint. Its actually more of an issue for Porcello than Erod. In Erod's case he either can throw his Change or he can't. If he can't it will take quite a bit of effort for him to get RH hitters out and a fair amount of assistance from the Catcher.
Porcello for his part actually has to pare down the pitches he is capable of throwing to the pitches he can throw successfully that day.
Vaz actually seems better at helping the Starter get through early decisions about what the Starter can throw successfully on a given day and might actually be a better choice for Rick and ERod. Whereas Sandy might well be better suited to Sale, and Nat for example. If I were Cora I might try Vaz with Rick once Nat is back so Sandy has two guys he catches regularly. Vaz just seems to work through the early decision phase better for Starters who are often stuck dealing with a different set of realities regarding their own pitch types every outing. The world totally chances for Rick and Erod stint to stint. That is not quite the way it is for Chris and for Nat.
Price is somewhere in the middle. Price is not often going to head out to the mound these days with neither his Change nor his Cutter. He might not have one of them. But he will not often have neither to rely upon and work off his FB.