Our company has multiple org, I just took possession one of those. I saw the following IP range in Profile Login IP range: 0.0.0.0 - 255.255.255.254. Is there a reasonable purpose to have that setting. Anyway any IP address hit that range. Or this's a Salesforce trick made for some purpose? I believe it is safe to remove it. Is that correct?
Yes. With that IP range users can connect from anywhere around the world. It is always a best practice to restrict to your own IP ranges. Usually some companies use it only on SandBox'es since they keep on refreshing. But for Production environment this has to be kept safe and potentially block users from accessing else where. By doing so you are adhering to your companies security policies. This is a bigger security key when it comes to integration.