First thing to understand is that a broker is an intermediary providing a platform to Buy & Sell whatever is available in the market place (Exchanges).
Therefore a Broker cannot block any contracts because of their whims & fancy as long as You as client have the necessary money to fulfill the contractual obligation & requirements.
Whichever broker blocks an available contract...take them to task send out an email to SEBI & the concerned exchange
SG
What you've stated should be the real position. But, unfortunately, in practice, it is not happening. The NSE has itself given facility to Brokers in the trading software to block trading of certain securities. Therefore, when somebody tries to trade in those securities, your order is rejected by the exchange with the message something like this "Trading of this security is blocked by your broker" (the actual language may be slightly different since I tried it and saw this language a few months back).
For example, a few months back, after devising an option strategy for third month options (after doing painstaking research and back-testing for about one full year's data), when I tried to place orders for selling the third month options (Reliance Money was my broker), my orders were continuously rejected with above message. Then I tried to buy the same third month option just to check whether the problem was with selling options; however, the same problem persisted and buy orders were also rejected. Thereafter, I spoke to Reliance people who informed me that they do not permit trading in third month options as a risk management measure since the volumes are thin. Even in Nifty where in fact the volumes are not so thin in third month options, the Reliance Money people refused to allow trading. Thereafter, I did not pursue the matter further. I didn't think of making a complaint with NSE since I felt that the NSE has itself given facility to brokers to block certain securities and moreover, I felt that I can try some other strategies as that was not the only strategy that can be successful.
But, I fully agree with your statement that the brokers should be made to allow trading in all listed options provided the client is willing to make payment for the margin or the purchase price, as the case may be. The ground of less liquidity does not make sense. It is like a chicken and egg story. Because there is (presumed to be) less liquidity in third and farther months' options, so you don't allow trading which further reduces the chances of increasing the liquidity. And, if you don't allow trading, how will the volumes grow which again means that you'll further restrict trading saying that the volumes are low. Why then have these far months' options in the first place, if the trading is to be restricted? How can trading volumes increase with such restrictions? It is for NSE to take a call which has listed such far months' options (I hope it is for trading and not for restricting trading as per sweet will of brokers). The situation in India is unlike US markets where you've very decent volumes in the farthest months' (or years', in fact) options of even several individual stocks. In India, we cannot have good volumes even in Nifty options for far months. One reason is this restriction business.
In fact, I fail to understand how risk management comes in the way if the client is willing to pay the margin for short sale or the purchase price for buying options, as the case may be? And, why did NSE permit listing of such options if there were issues of risk management? On the other hand, in fact, options are supposed to be instruments of managing risk in your underlying securities. Moreover, if they so want, they can have sufficient margins. But, why block trading if a client is interested?
Luckily, there are brokers who understand the things. For example, Zerodha is allowing trading in all listed options.