Does Russia have any benefits into keeping Chechnya?

In the days of the Russian Empire and then the Soviet Union the North Caucasus was important as a bridge to other Caucasian regions like Georgia, Armenia and Azerbaijan. So, it was strategically important to control the North Caucasus (including territories inhabited by the Chechens). It all changed by now. The region has no any value for Russia. To the contrary it's the source of all kinds of troubles and problems. Nonetheless Chechnya is an important element of Putin's home policy since it helps him to control and manipulate public opinion in the country. Don't forget that Putin came to power as a victor in the second Chechen war. Making peoples of the North Caucasus (including Chechens) clash against the rest of the population and then act as an impartial arbiter is Putin's trademark. Anyway, Chechnya and the North Caucasus as a whole must be separated from Russia.

Chechnya for Russia is like Afghanistan the United States. In the mid 90s it was a hot spot for Jihadist cells to operate in and still is today. You find Saudis, Jordanians, Egyptians, Syrians, Palestinians, who volunteer to go to Chechnya to become shahids (martyrs) for Jihad. It has more to do with oil, although it is important, it has now to do with keeping the country from falling in the hands of the Islamic extremists.