Why is it so important to prioritize?
Prioritizing can be important if you don't want to waste your time and/or don't want to miss your mark/deadlines.
When you prioritize you might actually be able to eliminate the need for other things or might make other things easier to accomplish.
In business, for example, you will need a CRM. It will track your clients, your marketing, your stats, etc. But you will also need several other things at or around the same time to be implemented. If you obtain the CRM first you make managing the marketing that you are also executing easier. If your execute your marketing first, it is fine, but then you waste a tone of time having to go back over everything so you can enter the data. Time lost on moving your business forward.
As for missing the mark. Let's say you have three deadlines. Deadline A in 2 weeks. Deadline B in 30 days. Deadline C in 3 weeks. You hate to do A and love to do B. Naturally, you engage in B first. You get lost in it, love it, do amazing work. But by the time you realize it, deadline A is past and deadline C is 2 days away. If you had prioritized based on the due date, it would have likely been able to meet all three deadlines.
Hope that makes sense.