Currently banks are selling products of not just their group companies but also others’. One example is HDFC Bank distributes not just insurance products from HDFC LIFE but also products from other insurance companies.
Also, why should RBI / SEBI influence group company interactions. In open market, such things are perfectly fine. What regulator can do is probably set some targets for selling such products from non group companies as well. Also, such captive distribution is not done free of charge. If HDFC Bank sells insurance & mutual fund products from HDFC LIFE & HDFC AMC, they will charge them both for such activities. As HDFC Bank itself is a listed company and would want to increase their own profitability, would they really charge less for HDFC AMC to sell their products compared to charges on other company products? That would not be taken well by the shareholders of HDFC Bank.