I'm not knowledgeable about your market or how your product works, just interested in technology and discussions here, so take this at face value.
To me your product looks like a service. I'm skeptical of any service that is a one-time payment versus some type of subscription. With a subscription I'm inclined to believe there's maintenance. With a one-time payment, I'm inclined to believe that either the product isn't sustainable without growth, will become ad-supported, or will fold.
Yes, I refuse to compete on price. One of my favorite phrases (just read it in a email an hour ago, in fact) is "your price is right on the edge of my budget."
How do I know that the main competitor isn't slowly going out of business at that price? Maybe their product is total crap, maybe I can offer stellar support that's worth a higher price, maybe I can guarantee GDPR compliance, maybe I can offer uptime guarantees, maybe my product is designed to a small niche that will pay a much higher price for a product targeted exactly at them, maybe I can focus on large customers who would be suspicious that a $4.99 price is way too low, maybe, maybe, maybe. In the end, ask yourself if you really think that $4.99/year * n_Customers computes to a number that makes it worthwhile for you.
> Also nothing should be priced at $4.99/year, I don't care what it is, if it's worth $4.99 a year then it's probably worth at least 20x that.
Would you still increase the price if the main competitor with the biggest market share is already cheaper (one-time payment of $5)?