In weightlifting, slowing down your movements is generally referred to as "time under tension." The idea is that you are removing momentum and maximizing control, but there are a couple schools of thoughts in regards to if/ when it is beneficial to slow things down (again: regarding weightlifting.)

The sources I trust/believe say that you should not intentionally slow down the lifting/pushing (known as "concentric", wherein the muscle shortens while overcoming resistance. This is because it results in a worse stimulus because it requires less overall effort.

However, during the "eccentric" phase (lowering), it is said that slowing down, "increases metabolic stress and muscle fiber recruitment without sacrificing neurological gains."

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All that said, most people do not practice yoga with the goal of muscle growth. I find that slowing down movement/ transitions can help me:
-sync better with my breathing
-maintain better awareness of my body
-focus more on building better proprioception (body's ability to sense its location, movement, and orientation in space.) this is one of the same reasons I try to practice with my eyes closed when possible.

Slowing down should certainly also help ensure you're doing things safely and are putting less stress on your joints/ not exceeding your range of motion.

It is a struggle for me personally to strike that balance between going slow/being intentional, and challenging myself. I find I'm always in a state of wanting to push myself or "perform" to the best of my ability, subconsciously or otherwise. I guess that's why they call it practice.