Is access to mining the only obstacle to centralised bitcoin-like currency? Considering the value of bitcoin beside dollars there seems to be so many applications where a centralised bitcoin-like system may be ideal for internal accountancy and transfers, especially among micro financial institutions.

Parsing a blockchain gives an overview of entire network.

If mining was restricted to only specific people what other obstacles are there for "private" use of Bitcoin clone?

Are there any commercial or opensource entities doing this?
Mining is the part of the decentralizing, to make a centralized currency you simply need to skip the publicly maintained blockchain portion, which includes mining. But without the publicly maintained blockchain, you really have only have a database that keeps track of transactions.