If you sell BTC and receive FIAT it is VERY likely that you will withdraw it. Because you "know" FIAT it's better/safer at the bank and you already have an account.
BUT
If you do the opposite: sell FIAT and buy BTC I believe that it is more likely that the you will leave it on the exchange (or the exchange's custodial "wallet") for long long time.
there is no difference. if someone sells X to Y and wants to hold Y then they will definitely withdraw Y and if anything if Y is bitcoin they can withdraw it a lot easier than withdrawing fiat since bitcoin withdrawal fees are a lot smaller (specially when the exchanges charge % fee for fiat withdrawals) and they don't involve banks so there is more privacy in that since the "user's" bank is not going to be involved in that withdrawal.
and conversely if the user wanted to keep trading they will not withdraw Y and they keep it on exchange to continue trading.
Not to mention that the Exchange's bank reserves are easier to check by the authorities (assuming a regulated exchange which most of them are nowadays). So it is much easier for them to get into trouble if they create fake FIAT balance.
there is nothing more transparent than bitcoin's blockchain. exchanges' cold storage addresses are mostly known and they could be looked at a lot easier.
It is way (probably multiple times?) easier for the exchanges to create fake BTC liquidity. Because of this their price pressure/manipulation capability is magnitudes higher on pushing BTC price down than on push it up.
i think the more important question you should be answering first is "WHY?".
exchanges make money from trades, so if the trading volume is higher they will make more money. that volume is always higher in bull markets when price is going up. so why would an exchange want to push the bitcoin price down? what would they gain?
Yes, there is nothing wrong with the Bitcoin blockchain itself. But knowing the exchange's hot/cold wallets is not too useful, as you don't know the other side of the balance, how much they owe their users.
To answer the why I would say money. It is free money and they keep doing the same money on trades too. So the two can go side-by-side.
I think one of the possible reasons to push price down is to wipe out margin trades an win big on that.
One other is to buy up cheap
BTC as if you push the price down you know it is cheap now. Hence you can buy (real) coins with created ones.