You should actually need less accesses against a recursive deck.
Way back in the mists of time when the Netrunner universe was young, someone did a little analysis that determined seventeen accesses would, on average, win you the game as the Runner. It is based on a few assumptions, but that serves as a useful little metric in general.
The most important assumption to note for now is that such a calculation is based on the raw agenda density of the starting deck. If the Corp is playing to score out agendas, that is not too unreasonable, since we can assume that every card type is equally quickly "used" when drawn (assets and ICE are installed, operations played, agendas scored or stolen). So the remaining cards available to access have the same agenda density as the original deck.
Contrast this with an endlessly recursive deck style which doesn't aim to score agendas in such a prompt fashion, but build board state to some win condition. To build the board state requires cards which aren't agendas. As the board state builds, the agenda density of the places you'd be running looking for agendas increases (you've taken out all the assets and ICE, but left all the agendas). So as the game progresses, you should need less and less accesses to win (less than the "standard" seventeen) as each access becomes more valuable.
Now, the one caveat is that you obviously have to be running the right places! The really useful thing that endless recursion lets you do as the Corp is play with where you keep your agendas. If you only run R&D, the Corp can hide all the agendas in HQ/Archives, for instance. If you lock down HQ, the Corp can quickly cycle any agendas drawn through Archives and back into R&D. So as the board state builds, the value of your runs on central servers improves, but in order to make sure you profit, you have to keep the Corp honest and make sure that you run all of them frequently enough. It's no use if the agenda density of HQ has massively increased and you keep running R&D (and if you keep running R&D only, HQ will get more dense because a sensible Corp isn't going to put those agendas back in R&D!).
That I think is the only real benefit of stopping the Corp clock and it relies on playing to the Runner's weakness, in the same way that a PE shell game player can adjust their play based on the reticence/overexuberance of a particular Runner. A clever Runner needs to mix up their central play.