I wasn't going off the notion that God is unapproachable ... it seems to me you are going off the notion that others who look to the one making the claim to provide evidence have themselves not done any "approaching". Let me explain: in my example with the Chupacabra I included different people who concluded different things based on different results. Some went looking and found something, some found nothing, etc. Lots of people who went looking came to various conclusions.
I've known some who "approached" for decades, and have said they found nothing close to what anyone claimed, or even what they had hoped to find themselves. Some who sought in earnest, giving over portions of their life to the "approach", some still have said they did not find anything.
And yet still ... I have known such people who did not close off the possibility entirely. Rather, they simply exhausted what they knew to do, thought they were supposed to do, etc. And eventually decided to try a different approach, to try and weed out conflicting claims, dashed hopes and expectations, the myriad of assertions and speculations and tail chasing, and instead they started looking at what the evidence we do have may suggest and say, and those who could actually provide a claim and support their claim with practical application, evidence, demonstration, etc. Thus, the "burden of proof" helps to cut through the nonsense and the talking heads. If I'm earnestly looking for something, for example, and I have 300 people all pointing their fingers in certain directions, the one I am more likely to follow is the one who can support their finger pointing with some type of evidence. Otherwise, what is to differentiate them from all the other voices claiming things with words ? As I said, it seems as though you are assuming that a person who places the burden of proof on the one making the claim "Isn't trying," and that is assuming an awful lot. Deffering (sp) to the burden of proof can be the RESULT of earnest efforts and trying, because when you step into the "Okay, I'm going to find out who God is," arena, what you find are millions of conflicting accounts and speculations. One way to "get to the point" is to ask, "Can anyone demonstrate what they're claiming or show evidence or proof ?" and furthermore ... to have it actually apply to reality in a practical way ? Otherwise, talk can be cheap. Even if the person talking is 100% accurate, talk can be cheap. I may have a million dollars back home, but if we need 10$ right now and neither of us have it, what good does that do us in the moment ? If someone comes along and says, "Well I got a 20$ right here, is that cool ?" ... guess who is being practical and helpful and letting us get from point A to point B.
The burden of proof being on the one making the claim is arguably a way that helps to facilitate the discovery and understanding of truth for a group, rather than just the individual who "believes". We exist as a group, not just individuals on our own islands. Thus it's helpful to have understanding and truth that we can practically recognize and apply for each other. The burden of proof can help to facilitate this as well as breed an environment for trust and integrity amongst those who want to know what may or may not actually be true and useful in reality.