It's not only natural, it's a good idea. Especially if you are crossing a large road.

I ride a motorcycle more often than not (see user name) and it's vital to ensure that the cross traffic is actually stopping when their light is red. You aren't "protected" because your light is green, and there's nothing physically stopping any asshole blowing the light and ramming into the side of you, probably without slowing down in the slightest first. That's because they're also staring at their phone. I can't even go a week anymore without watching some moron sail straight through a red light right in front of me such that if I hadn't spotted them first they would have run me over. And it's happening more and more often as drivers are more distracted than ever before. A couple of years ago I'd only see this sort of thing once every few months.