When I was involved with taking payments through paypal that's what we did. For us there was no value in keeping payments in there but there was plenty of risk. We stopped using them very quickly though, their fees were ridiculous.
This doesn't really help. When you link your bank account with PayPal the link is 2 way. I.e. PayPal can, without any input from you, transfer money out of your account. They can even do that if the account is empty. Your bank will almost certainly allow an overdraft on your account and you're still liable for the amount + overdraft fees.
I had some issues with PayPal about a year ago and a senior rep at my bank talked me through these details.
With my bank, it wasn't even possible to turn off the overdraft feature.
Bottom line is, PayPal almost always wins.
Or perhaps I am missing something here?
But yes, please remove overdraft from your accounts. I have no input to offer on paypal at this time.
P.S. Are you in the U.S.? I am just really surprised they bank deemed overdraft as a necessary feature in your case. I am personally interested in this case.
1. Overdrafting. My bank would not allow me to turn off overdrafting on my checking account; any money in my savings account would be used to cover an underfunded purchase from my debit card, causing a $25 fee and there was nothing I could do about this, short of closing my savings account or reducing the amount of money in it. Since free checking was dependent on a linked savings account with $500 minimum balance, this wasn't an option. The overdraft/fee could cause the savings account balance to go below the minimum, and if I didn't notice I'd get a $25 fee for my savings account as well.
2. The school would constantly charge my debit card as a credit card, and the transaction wouldn't appear for up to two days. Doesn't really help me keep track of my balance when transactions don't show up. Cashiers at the student store could usually process the card properly, but every time I bought something to eat at the cafeteria it would process as credit, regardless of what I told them.
Today, I think bank policies have changed (though I switched banks before this) and I believe you can disable overdrafting on most large banks (WF and BofA, anyways)
If you login during a vacation overseas and get your account locked, they keep everything in it. Doesn't matter if you never did any transactions yet and all that money is yours from the bank account you linked. If you get banned, you lose it. Getting your account and/or your money back is about the same level of difficulty as getting unbanned from a google account. It's not impossible, but be prepared to take them to court.
If you only use PayPal to purchase things online, the protection is great, but you don't want to be on the other end of that transaction.
Trying to get money from a real bank account (Lloyds in England) after moving out of the country was much harder though. It involved writing several letters and getting a policeman to stamp something, as well as multiple phone calls, including to several staff who gave me wrong advice. But still, they returned my money eventually.
You probably already knew that, but for the benefit of anyone reading this who didn't.