No, storing on OpenLedger is not the same as storing in a wallet, it is the same as storing on an exchange.

I am an active trader, so I do not move funds into and out of wallets often. I have coins I hold long term, and they may be in a wallet, but ones I am trading remain on the platform I am trading on unless I have another need for them. Keeping your money anywhere but your own pocket is always a risk. Most reputable exchanges do not charge anything but the standard fee to move money in and out. You will find high fees anywhere you can use fiat to purchase coins though.