Linking the card is primarily to give you (and Paypal) a fall-back option for funding your spending if your bank account doesn't have sufficient funds to process the charge. If the bank account has sufficient funds, it will work fine in many cases without a credit card.

If you have both linked (bank and a credit card), Paypal will transfer funds immediately, as Paypal knows it has an option for getting the funds if the bank has insufficient funds. However, if you have no credit card linked or remove your only card:

If you remove your only card and have a confirmed bank account, you’ll no longer be able to make instant bank payments. Instead they’ll be sent as eChecks, which take 3 to 4 working days to process.

This may not matter in many cases, but it may delay things some. There may also be services who require immediate payment (and won't support PayPal if it's not immediate).

There may also be some functional limitations. The one I see is primarily that some services that are geo-location-specific, Spotify for one example, use the credit card to verify that you are in a particular location (in Spotify's case, for licensing purposes). They don't seem to accept Paypal unless it's linked to a credit or debit card (even if it's verified via a bank account). I'm not sure if this is common with other services, but it's something to consider.