I have read that if the random nonce k used for the ECDSA signature is not chosen at random then someone can calculate the private key.
Is this really a problem in practice?
Yes, that's why clients like Bitcoin Core always use random values that for that reason.
Ref:
github.com/bitcoin/bitcoin/blob/master/src/key.cpp#L208-L234Reusing address doesn't necessarily mean that every transaction that you'll create will use the same nonce when producing signatures.
An address that you reuse may be a representation of the same script but it has nothing to do with the generation of k value when spending the multiple UTXOs linked to it.
Check the reference above for the function Bitcoin Core uses.