There is no universal answer. Of course a game company or a hobbiest should invest in supporting their customer. But the cost and effort involved is unique to every situation.
I see your point here. There's no point to have a 24/7 customer support team if the game is not very popular and only receives bug reports every few days or so. I agree that the developer can handle this by allotting part of his time. On the other hand, the same solution is not applicable for extremely popular games like, say, Candy Crush.
But how would you know if you can still handle it in-house or it's time to outsource a company?
If you ignore your early customers, you would be hurt in the long run.
I agree. Not only that, but it may lead to bad PR considering how people are in social media these days.