Certainly, it is not about the exchange but the coin itself. The trading volume will be good if the project is also good and has actual use case in the market. As we noticed, most coins without reason to exist, are finding it hard to improve their liquidity in the market. Most of the time, the dev team itself is the one creating the liquidity if they can't attract traders. And you will see it right away because they can't sustain its market. Whether, kucoin or binance or other small crypto-exchange, it is better to choose a valuable coin rather than go for a small cap coin, which is about to lose its value in the market.
This is 100% true, you could have a coin that could be disturbed with a small amount on Binance, check the lowest traded one and I am sure it is not really traded all that much, whereas check the small or medium range places and you will see the top one (usually btc/usdt) will not be disturbed even in those small places.
I have seen a place with around 4 million dollars trading volume total, and it had around 120 pairs, btc/usdt was around 3.2 million dollars there, so guess how the tiniest ones were, the smalls one had like 100-200 dollars volume. So, I have to say that it is not really that much of a problem of the exchange but problem of the pair.