I don't have any interviews to link, but the original intent behind invasions in Demon's Souls - that is, for weakened soul-form players to hunt down stronger body-form players and, in effect, kill them in order to steal their strength, adding an extra dimension beyond merely invading for fun, and even instilling a sense of desperation not only on the part of the prey but for the hunter too, something that could have been expanded on somehow in future games instead of neutered - is self-evident simply by looking at the game. The structure for it is fully in place, but the concept itself is wholly undermined, almost to the point of ruining it entirely, by some terrible design decisions. Namely, the existence of the Cling Ring, easily found at the very start of the game, that almost trivializes the HP loss on losing body form (albeit at the cost of a ring slot); and, of course, there is World Tendency: a brilliant idea so horribly executed that experienced players or even first-timers who read a WT guide should prefer to stay in soul form and even suicide in the Nexus upon regaining their body. Absurd. Thus, invading mostly boils down to organised duels and a bit of fun, making it nowhere near as interesting a mechanic as it could be.
Far from addressing the issue in Dark Souls, they made hollowing scarcely have any effect on the player bar disabling summoning; humanity trivial to farm; and hollows unable to even invade - the exact opposite of how it was in DeS! A wasted opportunity to bring coherent form to the original innovative DeS idea; invasions entirely boiled down to organised duels and a bit of fun [I suppose there's farming covenant rank ups too, though only really relevant for Darkmoon Blade and in my view not exactly exciting].
Dark Souls II reintroduced proper penalties on death but again trivialized them with Ring of Binding and later on scores of Rings of Life Protection. Duelling arenas became the focal point for PvP: invasions for a bit of fun*; ranking up in arenas for material reward. I think the latter reeks far too much of contemporary MMO PvP design (and all of the ills that that entails) and is incredibly far removed from the original vision of Souls PvP - a great shame.
*though admittedly the chaos of the Bell Towers was great for farming early game titanite; it's probably one of the best instances of players hunting down other players in order to make themselves stronger, which in a roundabout way is somewhat in the spirit of the original vision