But full node operator is unlikely to use such feature
Why? I guess node operators located in countries with strict legislation on illegal content, fearing legal action, would like to use that.
IMO those operator are more likely to use VPN or rent a server on country which doesn't persecute those who run full node.
and feature specific for Bitcoin Core doesn't need BIP.
It would be a protocol change, because currently OP_RETURN messages cannot (afaik) be completely ignored, they can only be pruned once validation of the block where they're located has been done. So it would need a BIP. Bitcoin Core as the reference implementation would be the first to have to support it. (Don't really get what you mean here.)
Now i understand what you mean. It'd require new service bits where node signal they doesn't store all OP_RETURN data. But as i said previously, i don't expect this kind of BIP/feature receive meaningful support.