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Out of topic...
Using services from any companies to move your Bitcoin when you don't have private keys hence full control on your coins are bad. Always had but it worse when Bitcoin rises and fees bump to the moon.
We all know that and it isn't the point in the original post. And NO, uing a web wallet isn't necessary bad. People can use it as an alternative wallet to make a purchase quickly for its convenience, their daily needs, etc... Instead to bother using a cold storage wallet.
You rely on those companies to set transaction fees for your transaction and you don't know how long they will wait to broadcast your transaction, in batch with the others. Certainly true that companies don't move your coin in a single one input one or two output transaction. They do batch transactions indeed. And you don't have option to replace it by higher fee...
It's not the point here, @OP is talking about a deposit problem and not a withdrawal