Anyone else uncomfortable with PayPal’s payment process?


I’ve been a PayPal user for about 7-10 years attached to the same bank account for me to receive payments. I recently sold an item and my bank account was nowhere to be found. Instead I found a PayPal procedure to attach an account so PayPal could send me my money.
The first question in the process is pretty easy - they wanted me to name the bank I want them to send my money. East Peasy. The next questions gave me pause. PayPal asked for the Name of my bank account and the Password.
Are all you people OK with PayPay having your private bank account name and password?
In the end, I requested PayPay mail me a check (5-10 working days for delivery).
toolbox149
I confirmed that what the OP described is something legit on the PayPal website. Login to PayPal and select Wallet on the top menu and "Link a Bank" (https://www.paypal.com/myaccount/money/banks/new)
Select a bank, then it will ask for a user/password login at the bank. PayPal’s description is:
We use Yodlee to confirm your bank details and to check your balance and transactions as needed, which can help your PayPal payments go through. For more information, see our Privacy Statement. You can turn off our use of Yodlee by removing permissions for this bank in your Profile.
There is an alternate option if you look at the bottom:
Link your bank another way (Takes 2-3 business days.)
In this case you would enter routing and account number.

PayPal is using Yodlee, a third party financial service (https://www.yodlee.com/company). Personally, I feel more comfortable using the traditional routing/account numbers.
“In the end, I requested PayPay mail me a check (5-10 working days for delivery).”

That’s impressive. I’ve tried the check route with PayPal with zero luck. The option always appears down or unavailable. 
Paypal has never asked for my password, been using them since 2000. Lots of scams out there and paypal is a favorite. When I did use them, got checks sent to me.