What this article isn't telling you is that DE razors can be almost as fast, but there's a learning curve. They don't flex, bend, or rotate to the right angle, so you must hold them at the right angle, even when you're going around curves. There's just one blade, so it's easy to apply too much pressure and give yourself razor burn, so you must learn to use minimal pressure. It takes time to learn these skills.
Is learning how to shave with a DE correctly and quickly worth saving money? If money is no concern for you, then no. However, there are other benefits. One pass of a five bladed razor is, you guessed it, five blades being dragged across your face, and likely with more pressure than is necessary given how much pressure is required just to make the flexing, rotating razor engage with your face. If skin irritation, ingrown hairs, etc. are a problem for you, then learning how to properly shave with a DE razor can dramatically reduce those problems. However, things may be worse at first while you're learning technique. This is all even more true if you're the sort who suffers from irritation and reuses cartridges too long to save a little money. Dull blades make skin irritation worse.
Another thing this article isn't mentioning is shaving soap. Most of us are used to chemical gel's or foams. To be blunt, they all smell awful and feel gross. Again, it takes slightly more time and a little technique must be learned, but traditional shave soap with a badger hair brush, lathered on the face, is something everyone should at least try. There are some awesome smelling soaps out there, and lathering on your face with a good badger brush feels amazing. If you hate shaving, this is a switch that might change your mind.
If you hate something, you can spend less time on it, or you can look for ways to make it more enjoyable.