This depends to some extent on the level of development of the country. However, in general, I do not think it is acceptable.
The power elite should not rule in a country like the United States. In a country like the US, the "regular people" have enough education and knowledge to be able to participate in governing. The country is well off enough that radical changes are not needed. In such a country a more democratic system is best.
In developing countries, it may sometimes be that a power elite should rule. The classic case for this would be a country like Singapore. As Singapore developed, it was run by Lee Kuan Yew and his associates. Their country started out poor and with a fairly uneducated population and needed radical change to modernize. That sort of program can be best pushed through by a less inclusive government that knows what is best for the country.
However, allowing power elites to rule is asking for trouble because they are likely to start to rule the country for their own benefit instead of for the benefit of all the people.