Has the separation of powers and check and balances built into the Constitution limited government, or made it too accessible to citizens?
It certainly has achieved its goal of limiting the power of the various branches of government. Just look at the gridlock we are in now. We desperately need to make headway in several areas, but without a dominant party with a large enough base, we are mostly spinning our wheels. Maybe, in the long run, that will turn out to be a good thing. At least we haven't produced any Adolph Hitlers or Joseph Stalins yet.
The checks and balances have generally been successful in keeping the individual branches of the government equal. However, there seems to have been a trend lately to lock the executive and legislative branch in political struggle while devaluing the legislative branch.
I do not think that it makes the government too accessible to citizens. Citizens (through interest groups and such) still have a great deal of influence on government even in a system like that of Great Britain where there are not really any checks and balances. Therefore, I don't think you can say the system is responsible for allowing too much access to citizens (if there really is such a thing).
I would argue that the point of the checks and balances is, at least in part, to limit government. Remember that when the system was designed, the people were under the tyrannical rule of a king. They wanted some say so in their own laws and government. The system of checks and balances was designed to keep one branch of the government from gaining too much power. Everyone answers to someone else and that keeps any one person or group from gaining an advantage. That's the idea anyway. This type of system does limit government. It is certainly slower to move through political channels rather than have one person who can make an instant decision. In many ways, our government is limited; however, that isn't necessarily a bad thing.