"What I mean by that is that each vocal line is different but connected to each other."
Wait are you talking about harmony here? Sorry if it seems like I'm being obtuse here but you're not doing a great job of describing this whole "flowing melodic line" thing. Maybe you could provide a specific Beatles song (or section of a song) as an example?
The Stones are more of a blues band than a pop band so they arguably shouldn't be held to the standard as the other groups you mentioned (yeah most early Genesis ain't pop either but they still placed a stone emphasis on melody, especially compared to most major prog groups)