You appear to be taking your spouse's statements and requests at face value, but in my experience, statements and requests like this from a SO often mean something quite different than their direct content. You cited:
"I'm afraid you'll leave me some day."
"If you're ever thinking of leaving me, tell me immediately."
This kind of statement usually is a semaphore signalling that in the recent past you have not been meeting her needs. She is not worried about the future as much as she is telling you that you have not made her feel safe and secure now or in the immediate past.
Typically when people ask for this kind of reassurance they are responding to a specific interaction or pattern of interactions that bothered them.
You say you don't believe you have control over your future behavior and you don't want to just make the conventional promises that reiterate spousal vows. That's actually great because now you can be extra-motivated to have the conversation your spouse likely really wants and needs.
I mean the non-defensive conversation where you learn what you've said or done (or failed to say or do) that prompted her feelings of insecurity, and what you can do to avoid hurting her in that way in the future (assuming you want to do so).
Then when you follow through by changing your own behavior to provide whatever nurturing interaction she is craving, you'll almost certainly see a different behavior from her as well.
If after trying you still find that you and your spouse cannot achieve a balance in which she feels safe and secure with you all the time, that would be a good time to get a teensy bit of outside help. A good family therapist specializing in brief, outcomes-focused therapy can sort this kind of thing out in two or three sessions, with a happier and more confident couple as the result.
Edit: Additional Technical Discussion:
When I say that your spouse's anxieties arise from some situation in which you have not met her needs, I don't mean to imply that you have been neglectful or done anything wrong. I mean only the literal fact of the matter. You may not have been able to guess what her needs are, and she may not even be aware of what they are. They may be triggers or situations that come from the past.
I say this because what your spouse is experiencing sounds like what is sometimes called Anticipatory Anxiety, or anxiety about things that might happen in the future. This type of anxiety is typically associated with prior experiences that may have occurred at any time earlier in life.
Important life experiences lead to the formation of neuronal connections in such a way that subtle and specific sensory inputs may trigger a cascade of autonomic nervous system activation along with "memorized" feelings and thoughts. This is why a particular song or scent can trigger intense feelings and memories.
When we look closely at unwanted responses triggered by a stimulus, we often find that they were adaptive (helpful) at the time they were formed, but have become maladaptive at a later place and time. For example, fear of abandonment may be adaptive if it keeps a child from straying too far from her parents, but maladaptive if it prevents her from being confident in an adult relationship.
This kind of stimulus-response pattern is described differently in different models of therapy, but at its roots it always comes down to the same thing: some kinds of triggers lead to thoughts, feelings, behaviors, and internal physiological changes that may be out of proportion to the triggers themselves and the context in which they appear.
When this becomes a problem, there are a number of therapeutic approaches that can help. The literature seems to indicate that pure cognitive therapy (talking about it) is the least successful in resolving this kind of trigger-outcome mismatch, because the unwanted thoughts are not the cause of the problem, but the result of it. The most rapidly successful therapeutic approaches seem to be those that identify the triggers and either desensitize or depotentiate them, so they no longer cause the unwanted response.
Anybody who wants to learn more about this model for understanding unwanted responses like anticipatory anxiety can read about the family therapy work of Virginia Satir (link to Wikipedia page about Virginia Satir) and the work of Richard Bandler and John Grinder who studied her techniques and developed a descriptive formalism. Although their approach to understanding and modifying human contextual response has been vigorously disputed by practitioners who have embraced other models, single-neuron brain studies have recently validated the fundamental concept that sensory triggers can evoke maladaptive learned responses, and that those triggers can be depotentiated and even remapped (very quickly) with specific sensory exercises, both in rats and in humans. You can read about this in a scientific paper called Extinction of Learned Fear Induces Hippocampal Place Cell Remapping.