OP why are you shying away from having full access? Blockchain company's usually make use of kyc so as to avoid impersonation or an intruder from having access into your wallet as they may not have the informations you provided during kyc process which is why the kyc it's in your best interest. Another way is that you will need contact their customer support , that's if you have all day.
I've been using blockchain for so many years and so are my relatives for the last 10 months there's always been a pop-up asking us to verify so we can use the trading features of the wallet, I can still use my wallet for sending, and receiving and they are not limiting or forcing me to verify because I never get over their threshold limit.
The key to continuing using your account without having to go through verification if you don't want to go through that is to never use Blockchain in storing a big amount, the biggest amount I stored on Blockchain was $150 a month, make Exodus and Electrum your main wallet, they also have an exchange feature, don't let any wallet limited you for accessing your coin use a noncustodial wallet.
If they force us to verify, and we don't want to lose our privacy, then I think we can completely switch to a non-custodial wallet like Electrum and stop using blockchain wallets because using multiple wallets won't do any good.
Blockchain.com wallet is the first wallet I used when I first entered the market, and as a newbie, I didn't notice that they collect personal data but when I realized it I stopped using them and switched to Electrum and I am very happy with Electrum.
If we accept KYC, then use a centralized exchange, they will provide a full range of different services for us. For long-term asset storage, we should and should only choose non-custodial wallets.
