Let's discuss the benefits of ignoring their messages:
1. You're freed from constant thoughts about how to reply. You're not obsessed with these stages and various hypothetical situations. It's straightforward: if they wish to reconcile, they will find a way to mend what's broken. That's their responsibility. As evidenced in my practice, if an ex truly wants to reconcile, they will literally show up at your doorstep. A mere ignored message won't deter them.
2. It increases their uncertainty about you and accelerates nostalgia. The lack of information breeds immense curiosity.
3. You mitigate the risk of responding in a way that signifies you're still in a weak (one-down) position, which would repel them. Here's the secret from practice: simply responding to someone who chose to leave, especially if the message isn't about reconciliation, signals dependency. Even a neutral message could be perceived as such.
Could ignoring their messages push them away? While I haven't seen such cases, I believe there's a small possibility. However, an improper response can and will push them away. If they send you a message and you perceive it as a step towards reconciliation, then you reciprocate by moving a step or two towards them (instead of, for example, allowing them space to progress by making a tactical step back), they will pull away. They may even regress to Stage 1 of no contact, where they experience relief from the end of the relationship.
So, in my experience,
ignoring any message except those from Stage 5 is the most efficient recovery strategy.