Right. Okay. I don't usually reply to comments but here we go...
First off, sure, loki gets a kick in the nuts a few times. Not exactly fun, that's true. But this is the guy who was thrown around by the hulk and was cracking jokes like five minutes after. It's fair to say that would not have been too painful for Loki, relatively speaking. To be fair, I have not been kneed in the balls so I can't speak, but I'm almost certain that being shaken like a rag doll by hulk, or enduring systematic torture from Thanos, or being hit with mjolnir would have been a lot more painful. Also, is loki experiencing new pain or just reliving the memory of pain from when this originally happened?
Secondly, Mobius was definitely being monitored. Or, at the very least, believed he was. "Timekeepers are watching" is a hint that Mobius believes that his every action was being watched. Also, if a time cell is meant to be the TVA's prison cell, then surely these would be under constant supervision to make sure their prisoners weren't trying to escape? Probably not a coincidence that Renslayer was waiting for Mobius the second he and loki exited the time cell. Even though she knew Mobius had switched the tempads, she knew immediately knew that Mobius was planning on betraying the TVA. And hunter B15 took Sylvie to an apocalypse, not a time cell when asking her about the memories as apocalypses are proven TVA blind spots while time cells are not. Mobius had to choose a memory that appeared to demonstrate how he was "working his loki". Don't think he could have gotten away with a memory of loki playing with a load of puppies or going to town on a big pile of nuts and grapes.
My main point concerns why Mobius picked a memory where loki is told he will always be alone. Obviously, this isn't exactly pleasant but, presumably loki has heard way worse. His own adopted father told him is birth right was to die, for example. (After this variants nexus event but I would bet Odin has been saying this type of shit to loki for centuries.) This is coming from Sif who Loki doesn't exactly hold in high regard so I doubt he really cares what she thinks. In fact, apart from his family, loki doesn't really care about what most of Asgard thinks about him which could be an essay in itself. Loki even says this himself, by stating he never thought about it ever again. This bit is my really main point, I promise. Mobius wants loki to think about Sif's words, to consider if he really deserves to be alone. In my opinion, loki didn't think about Sif's words because he believed them and accepted that he would be alone. We never see him form any relationships, romantic or otherwise, and he even admits that he betrays his family which leads to the breakdown of these relationships too. Loki believes he deserves to be alone so does nothing to maintain relationships. Until Mobius.
Whether you ship them or not, Mobius and Sylvie are the first relationships we see Loki fight to preserve. When Mobius asks Loki if he believes he deserves to be alone, loki sates he is unsure. However, by the end of the episode Loki is willing to tell Sylvie his feelings for her, something which is 'new' to him after previously denying his relationship with her to Mobius. He also goes on to acknowledge his friendship with Mobius. For the first time, we see Loki actively trying to build relationships with those around him rather than push them away.
Mobius wanted loki to accept that he is worthy of love and happiness. That is why he put him in that time cell. Loki needed to re-evaluate his internalised self-hatred so that he could embrace the new relationships being extended to him... Small price to pay for a knee to the bollucks in my opinion...