India is climbing down, so it's a moot point, but even in the event of war, there is zero need for Chinese civilian shipping to tip toe around in the Indian Ocean.
The Indian 'analysist' who suggested the idea is a pure moron, plain and simple, as he clearly doesn't understand how international trade works.
Even if India only targeted Chinese flagged civilian cargo ships, that will open up Pandora's box for them, as that will make it impossible for any of their western cheerleaders to offer them even token verbal support, and it will make all Indian military and civilian ships fair game for the Chinese.
The PLAN can sit a thousand miles off the Indian coast and rain cruise missiles on their ports and key infrastructure with impunity while PLAN subs can wreak havoc to the Indian fleet closer to shore and also covertly sow mine fields off the Indian coast, and all in the name of defending freedom of navigation.
Any Indian island bases use to attack Chinese civilian shipping can be easily cut off from supply and reinforcements. After they have been starved half to death and bombard to hell and back, the PLAN can use them to practice amphibious assault for real.
Even if China doesn't keep those islands outright, a condition to their return to India will be that they can never again be used for any military activity, with a Chinese or UN monitoring force in place if needs be.
A boarder war in the Himalayan boarders will be massively humiliating and crippling for the Indian military, but minimally damaging to India as a whole.
However, a free-for-all open war (India attacked Chinese civilian ships in international waters first, thus making Indian civilian infrastructure fair game for Chinese reprisals) on India's coasts could quite easily set Indian economic and social development back by decades. Just how bad will depend entirely on how much China wants to hurt them.
TBH, I think one of the reasons China held back in Donglang was because a fight there would give China very limited scope to truly hurt India.
With how biased the west is, any war involving China, irrespective of the actual facts, will get blamed on China, with all the usual China-threat 'intellectual' prostitutes swarming out of the woodworks to spew their party line lies.
China would pay a big reputational damage for a mild slap on the wrists for India, which hardly seem worth China's while.
However, if India gift-wrapped such a golden opportunity for China to effectively eliminate India as any remotely credible possible future competitor for the next several decades or even century, well, China might well just take India up on that offer.