This part is called "the crystal".
Acrylic is actually a great material for this. It's better, in my opinion, than glass, albeit not as good as synthetic sapphire, the other popular, but more costly, material used for watch crystals.
The reason I like acrylic better than glass is that while it scratches more easily, it's also repolished more easily. There's a polishing paste made just for acrylic, called Polywatch, which works great. Glass is harder, but once it scratches you can't remove those scratches. Acrylic can also handle sharp blows pretty well, since it can flex a bit. Sapphire, of course, isn't something you can readily polish at home, but since it's much, much harder than even hardened glass, it's virtually scratch proof, but glass is sort of a bad in-between where it's soft enough it can scratch, but too hard to easily restore.
So, watch crystal materials in order of my preference are sapphire, then acrylic, and then glass bringing up a distant third. If you can't be so hard as to be nearly invincible, the next best thing is to be soft enough to absorb blows and be readily restored. And, should it take too much damage, acrylic is inexpensive to have replaced with a new acrylic crystal.
So, I wouldn't worry about it. I have 50 year old watches that still have their original acrylic crystals, they just need a light polish now and then, maybe once every several years, to keep them clear and easy to read.