There's no in-universe reason, but Toriyama intended for the transformation to make Gokuu look scary. Fat Boo says that Gokuu looks scary when he first sees Super Saiyan 3. Zenoh also says that Super Saiyan 3 looks scary. Plus, Vegeeta has the same face in Ultra Ego; Gokuu nicknamed that form "Freaky Face".
But I think SS3 was modeled a bit after Oh-zaru, which also lacks eyebrows. One of Toriyama's concept sketches of SS3 featured a tail:
![940duf5ahfp81.jpg 940duf5ahfp81.jpg](https://dbzeta.net/data/attachments/4/4486-b005e0513f19cce3bf630a1bd2c896dc.jpg)
And we see Oh-zaru during the transformation in the anime; Gokuu even looks SS4-ish at one point (I'm pretty sure Toei got the idea to make SS4 from this):
![svlrbbu9uaxd1.jpeg svlrbbu9uaxd1.jpeg](https://dbzeta.net/data/attachments/4/4487-f3594cdc1b621910cd935a9c6cd91e15.jpg)
Gokuu looks like a Neanderthal in SS3, which makes him look like he's returned to an earlier state in human/Saiyan evolution.