I have no idea if LL is guilty or innocent, but discussing the theory of staying close to the crimes, yes it absolutely does happen. It is thought they get a thrill from a sort of god like control.
One of the most prominent theories is the desire for a psychological high. They create the crisis. By causing a baby to collapse, she could have created high-stakes medical emergency where she could be seen "fighting" to save them.
Prosecutors argued she enjoyed the "excitement" of the resuscitation attempts. She was often noted to be present and unusually calm or even "excited" during these life-or-death moments. This could of course have been an uncomfortable reaction in the case of LL, a nurse struggling with the deaths, and feeling torn up that she could not infact save the babies.
Digital "Stalking" of Victims' families, while some killers return to a physical location, Letby "visited" her victims through social media. Evidence showed she searched for the parents of her victims on Facebook dozens of times, including on anniversaries the infants' deaths or on Christmas Day for example. This allowed her to witness the ongoing grief of the families from a distance, sustaining the "high" or sense of power she felt during the crimes long after the events occurred. This could again be linked to a mental health struggle in LL, and a feeling of letting the families down.
She injected herself into the grief, and didn’t just distance herself after a death; she often stayed intimately involved.
Some may view LL as a "supportive, grieving nurse" while being the actual cause of the tragedy. It provides a unique power trip for some serial killers, being the person the family leans on for comfort while being the one who destroyed them.
Again, no idea if LL is guilty or innocent, the acts may have stemmed from a misguided attempt to comfort, and mental health struggles with being around such sick babies, and feeling guilt at being unable to save the babies.
However that all being said, the idea that murderers always distance themselves from their crimes is absolutely untrue.