Let’s say americans don’t understand what their rights to speech mean. It doesn’t matter since you didn’t repudiate the fact that they may have stronger speech rights.
You are glad that you don’t have the right to bear arms. But that does not seem to me to refute that a constitution is important to prevent erosion of rights or that the US is ahead in terms of rights. Just that you personally don’t care about that right.
Finally, you state that in the U.K there is also a protection from unreasonable search. Fair enough. But is it stronger than what is in the US? Is it protected in form of a constitutional right or just a law that can be repealed at any time?
The strongest argument is that despite these apparent constitutional guarantees, it has not prevented police from infringing on these rights. I would agree. But that seems to me to be an issue of enforcement. Not having these would mean there would be no legal basis to change police behavior, only a social impetus. That may be enough but I would like to have both options.