No. You can check less things, than existing nodes, and stay compatible with the rest of the network. For example: if some client would handle only P2PK, and would mark everything else as valid, then it would successfully synchronize the whole chain. The same is true for a client, which would check the correctness of the merkle tree construction, without checking any underlying transaction data.

Also, you don't need the full UTXO set to check, if new blocks are valid or not. Instead, clients could require ZK-proofs for each transaction input, and never store the history, but only the proof, that it is correct. Which means, that the full chain is required only in the current full node implementation, and it can be changed in the future.

The same is true about data compression: if you have weak public key, which is reused hundreds of times, then you don't have to send it over and over again. The protocol does not require anyone to do anything like that. The whole historical chain can for example be passed in much more compressed form than today, and such nodes can stay compatible with existing ones.

An extreme example is header-only client: you can trace only block headers, and not much more than that. Then, everything else you can handle through ZK-proofs or other kind of proofs, and still check, if new blocks are valid or not. Maybe even going further is possible, but each proof comes with some cryptographic assumptions, so storing all headers is highly recommended, as long as we don't have many billions of blocks.

So, to sum up: things can be simplified in future versions, without affecting existing implementations. Then, current node runners can still process and store hundreds of gigabytes, while new, more lightweight nodes can be set up successfully, and be more resistant to spam, or allow processing more transactions per second, while being compatible with the rest of the network.