Value is just what people think something is worth, it's a shared illusion, not an intrinsic property of ... anything much.
Having a static, fixed supply and independence from central control makes something valuable to you, not so much to me.
>If the supply of BTC was infinite, it would have essentially no value
But there are many other circumstances that could result in BTC having no value, regardless of scarcity. For instance if people stopped using it, at all. There would be no value in being the only one with bitcoin, regardless of how scarce they are.
edit: Probably not the best example, but either way, value is a perception.