It does matter: FDIC insurance protects you as a depositor specifically from counterparty risk, i.e., the risk that your bank may become insolvent and fail to honor your withdrawals. But in the crypto world, if you move your crypto off an exchange (your counterparty) and onto your private wallet, then you've eliminated your counterparty risk by eliminating your counterparty.

Obviously handling your own crypto custody in a private wallet means you're taking on a whole different set of risks. But the key feature of deposit insurance is that it mitigates a risk factor that's both 1) opaque to you, and 2) outside your ability to directly influence. And these are properties many crypto-aligned folks care about.

It does. When coinbase goes bankrupt, they can liquidate all user assets. User assets at banks are insured up to 250k.

Why should I take the risk of a company going bankrupt and liquidating my funds when I can keep the money in my house (wallet)?