I believe developed countries can exist without some kind of government welfare. I have my doubts many people would want to be in that country. I feel like a country that overlooks the poor in their country is going to have a difficult time sustaining control, but that doesn't mean it is impossible.
Yes, I think that any developed country can exist without some kind of government welfare, because that is how the United States got rich in the first place. The United States was the first country without a safety net, and in which people were left to themselves without regulations. And in that environment we all thrived.
A society could be make it or break it. Survival instincts are real, and the desire to live a more comfortable life is very motivating. That desire exists today and is exactly why so many illegally immigrate into the United States.
The problem is that if you strip all welfare programs of any kind it hurts the poor. Now, to be frank I'm not concerned with an adult that made very poor (and repetitive) choices that put them in a position of misery. It's the children of those individuals that deserve a chance. But it's a repeating cycle, and the current system is broken by continuing to let this to happen.
I fear now that at least in the US welfare is here to stay. Many of the jobs that used to provide food and shelter for many people are now gone, thanks to bad trade agreements.
The people of a civilized nation do not need government welfare to survive. The first welfare programs in America were added in the early 1900s, but before then America was already one of the most successful nations in the world economically. American entrepreneurs and businessmen were creating plenty of wealth and innovation. Even before welfare programs the poor already were doing better in America (with its demonized unrestricted capitalism and big businessmen) that any other civilized country at the time. If a developed nation can prosper without welfare, it's safe to assume that one can at least exist without welfare.
A government implies the institution of a military in today' modern world, which some might view as a kind of government welfare. That aside, militarily armed nations seek self interested advantage, which implies competition and inequality. This kind of inequality need be addressed through policy, if we are to accept the validity of the nation state, in order to preserve domestic tranquility in the face of hard times.
I do not think that any government can exist without a government welfare program. I think that such programs should exist to help those that cannot currently help themselves. The flaw in the system however is that it allows some people to live off the program for the rest of their lives, which is something that needs to be fixed.
I'm not saying it's impossible, but it would be unlikely enough that it wouldn't be a possibility worth considering. With no one person or group of people making the big decisions and keeping order, not only would there be chaos, but there would be a constant struggle for political power and eventually the nation would split up into many different smaller countries, each with a government. Though government can seem like an inconvenience at times, it is more than necessary in the world we live in today.