Frankly no Coast Guard travels thousands of kms for patrol duties. It's limited to the littorals of the home country , hence the name Coast Guard . Patrolling waters off the coasts of Mauritius , Seychelles etc is not our responsibility & if it's deemed so , it should be handled by the IN .
Logically all our coastal waters upto 3 kms should be the preserve of the Marine Police in those respective states followed by littoral waters up until the first 100-200 kms depending on the threat perception & assessment by the ICG , followed by the IN in waters beyond that .
The proposal for a marine police was made by a committee looked to investigate the security loopholes that facilitated the 26/11 terrorist attacks & suggest remedies. Like most things in Mera Bharat Mahaan , it remains WiP that too 50% of the case .
The ICG has been considerably strengthened leaving the IN free to move into deeper waters & choke points conduct joint exercises with foreign navies building up a rapport with them , map the oceans etc . This too has taken some 13+ yrs .
As regards the Marine Police which comes under the jurisdiction of the state government , the less said the better.