The larger a country is the larger the bureaucracy is and the less efficient it is. Smaller governments are more flexible, more responsive, and represent the people better. When governments control many people and regions, one size fits all solutions never work well across the board. Smaller countries tend have a more closely related population in terms of culture, economic and social standing, and history. Because of this the government will better serve a smaller population.
No, I do not think that breaking lager states into smaller ones will be beneficial for a country's progress. I can only speak for the United States of America, but if we broke our larger states into smaller ones it would just make things more confusing. It would actually slow down progress.
Whether it is a small state like Sikkim or a big one like Bihar, good governance depends on the extent to which power is devolved. You have seen it in a big state like Madhya Pradesh under Digvijay Singh and a smaller state like Bihar under Nitish Kumar. It has to do with devolution of powers rather than anything else. There are many smaller states but do you see size guaranteeing their development? Again, if a large state has an enlightened leadership that sees merit in devolution of power, things move forward and people are better off with regard to access to basic goods and services.