In this case, probably the best idea is to contact that third party to increase the transaction fee or if someone still wants or has to use third party, it's the best to avoid Bitcoin transaction in this case because these exchanges always send with very low fee and instead, one should choose Ripple or Nano or probably Bitcoin cash or Litecoin, depends how limited he is to options.
Which coin is Nano?
Because of low transaction fee, someone should hold altcoin instead?
Exchanges processed bitcoin transaction fast, the huge withdrawal fee demanded for is more than enough to make the exchanges to use high transaction fee.
Nano is not a famous coin but it does its job. Instead, you can use XRP.
And your second question sounds kinda strange. Personally, I have no problem with using bitcoin, it fulfills my needs but there are cases when you may prefer to use altcoins.
For example, imagine you have Tron in your wallet and you have to buy something from website that has built-in coinbase payment gateway and your only option is to exchange Tron to coins that are accepted by Coinbase, what would you do? If you exchange Tron to Bitcoin address given by coinbase, then there is a chance that instant exchange may send it with low transaction fee and you'll have to wait hours to get 2 confirmation. In this case, it's best to exchange Tron to XRP address that's given by Coinbase and get your transaction done quickly and finish your order ASAP.
But I have noticed that some exchanges send transaction with enabled RBF feature. In this case, probably the best idea is to contact that third party to increase the transaction fee
Although this is not exactly what Loyce was talking about but I've never heard of someone complaining about n exchange withdrawal transaction being stuck for too long. Most reputable exchanges process withdrawal transactions in batches and they pay more than enough fee for a fast confirmation. In fact, fee overpayments by exchanges are the main reason why the mempool get congested every now and then.
I don't mean exchanges like Binance and Coinbase, they spend transactions with good fee rates. I mean small instant exchanges that you can see on Bestchange.
This is so right, and having RBF feature on an exchange sounds like overbearing and just a bragging feature that it can be used but in fact it's not. Also, i never heard any exchange have it, it might be better mentioning it here.
It may sound overbearing but you can actually see that transactions from exchanges have RBF enabled. For example, check FixedFloat. Transactions from FF have RBF enabled and fees are sometimes very low.