I agree, should. But ruling precedent by judges has said otherwise, that the request for a lawyer must be clear and unambiguous. It should not be a question, speculation about the need for a lawyer, "I think I need to..".
Yes, this is unfortunate. Especially considering the way the US very broadly interprets rights under other amendments, yet so very narrowly in the case of the 6th amendment.
Why not just give every suspect a lawyer immediately. And since any sane suspect will listen to their lawyer (who will advise them to plead the 5th), why not ban police from interviewing suspects altogether, and simply give a list of questions to their lawyer to discuss.
Only reason we don't is that its obviously too expensive and impractical. This is why we initially try without, and involve a lawyer when "it gets serious".
So consider this: Why should the suspect be punished for this reality?